A few tricks I've learned with spray adhesive over the years:
1. Not all spray adhesives are created equal. Stickiness and open/work time vary greatly among brands and models. Some are designed for good adhesion, while others are designed for art that might be de-mounted at a future date. "Spray Mount" is a common name for lower tack adhesive used for art.
2. Spray the paper, not the wood. This reduces the amount of liquid glue that contacts the wood. Only the drier, congealed, less sticky glue will contact it.
3. Experiment with drying times. There are numerous variables to drying time:
* The adhesive brand/model
* Room temperature
* Room humidity
* Product temperature
* Work temperature
* Application thickness (how much you put on!)
4. Experiment with application thickness. A light coat may not have as much initial tack as a heavy coat, but it may dry too fast to get to the low tack portion of the drying.
I've experienced 30 second to 15 minute or more drying times depending all these variables, and a single can of adhesive can produce wildly different results. Also, longer drying times usually imply better dimensional stability which is important to a pattern. A heavy coat of super gooey adhesive will wrinkle paper much worse than a light layer of low tack in my experience... not good if you're trying to cut wooden clock gears.