A few more remarks now that I have a bit more time.
If 1/4" (6.35mm) bits do not fit your router then it may use European 6mm bits, which will have a very slightly narrower shank than 1/4", or 8mm bits, which have a considerably larger diameter shank than 1/4" (12mm is also common in Europe and is roughly equivalent to our 1/2”, or 12.7mm, shank bits). I suspect that many 1 to 1-1/2 HP routers of the era would likely fit the duplicator as many were based upon the dimensions established by the venerable Porter Cable 690 series router of that period (somewhere packed away still I have several brands of routers from the 70s, 80s, and 90s all of which are largely, if not completely, compatible with my old 1-1/2 HP PC 690 router and it's fixed and plunge bases of the era). Some routers incorporate replaceable collets such that you could replace a 6mm collet with a 1/4" collet, for example, while many cheaper low-end routers often milled the collet directly onto the motor shaft and is, thus, irreplaceable (I would expect the B&D to be in this latter group of fixed collet routers).
What you are trying to duplicate is a very common electronics project box and they are widely available in both plastic and aluminum in a wide variety of sizes for usually quite reasonable prices (particularly relative to trying to manufacture such for yourself), even more so in the secondary, surplus, or Chinese markets. If your goal is to recreate such in wood then be aware that you will need to modify the wall thicknesses as wood is not a perfectly uniform material and can flex quite a lot at such thin thicknesses, it will also tend towards being brittle at those dimensions since many woods can cleave relatively easily both with and across the grain (ray cell faults run perpendicular to the grain) when so thin, particularly if using certain species of wood -- in thicker materials those are not usually of great concern but they become increasingly important at very short or narrow dimensions (some species being far more prone than others).
If it is simply the wood look that interests you most, you can finish a plastic or aluminum box with a faux grain pattern to simulate the wood appearance and it can be rather convincing to those not intimately familiar with wood when done right. Such faux finishes are frequently used to make metal and fiberglass doors appear as if they were wood. You can find instructional guides and the special wood grain applicator online pretty easily.
But also keep in mind what those duplicators were intended to replicate. They were meant to roughly duplicate 3 dimensional relief carvings and other fairly shallow works. I don't know that they have the sort of rigidity and absolute precision and parallelism necessary to reliably recreate the box you are trying to duplicate.
If you really want or need that box in wood, you will almost certainly find it much easier to create by hand on a router table with carefully (and rigidly secured) stops and then gradually mill away up to a couple of millimeters of depth with each pass (how much per pass will depend upon the characteristics of the wood you wish to use and the diameter of your bit's cutters). The best bit for roughing out is an upcut spiral bit as they are not prone to catching on grain and they will draw most of the waste below the router table (where ideally you would have a dust collector to catch that waste). The same for the lip around the lid, though you will find it far easier if you drop the rounded cove/corner sections of the lip -- just mill them as a square box shaped lip and make the walls thick enough to accommodate four small neodymium magnets, one per corner 1/8", 3/16", and 1/4" neodymium magnets are all easy enough to come by both in craft supply shops as well as online and are inexpensive. However, you will find life far easier if you make the sides out of flat stock and then finger-joint the four sides together.
I would suggest a minimum walk thickness of 3/16" for most hardwoods, at least 1/4" for the top (to allow for a 1/16 to 3/32" raised interior lip) with a lip width of around 3/32" so that it is not too fragile, and a bottom thickness of 1/8" (if trapped in dados) to 3/16". You can then go any of several routes to attach the bottom -- a rabbeted ledge, a routed dado to trap the bottom in, or glue blocks into the four corners of the box and glue, screw, or nail the bottom in place (corner blocks would also allow thinner walls yet still allow for decent sized magnets at the corners if you wish. I know such is quite doable as I have made such boxes myself using just a router table to route the box and a tablesaw if building the walls and bottom from flat panels and finger jointing them with 1/8" or 3/32" fingers (base the finger width upon the width of your chosen tablesaw blade, ideally a blade with flat-top grind teeth or a mix of ATB plus flat-top teeth) -- a fingervjointing jig is easy to make for your tablesaw and attaches to your miter gauge to index each finger. A jointer and thickness planer are also desirable to square and flatten your panels, though not absolutely necessary, and a bandsaw is very desirable if making boxes more than around 3" deep.
An even easier, albeit much more expensive, route is to use a good CNC machine to mill such a box from a blank of wood as that is what CNC excels at doing as a good CNC will be both stout (rigid) enough and have the necessary positioning accuracy to mill such a box with a mote than acceptable success rate. It gets more iffy and may require more tries if using cheaper CNCs as you do largely get what you pay for in a CNC machine (generally speaking, though the lower end has been making improvements with each new year).
Best of luck!