Wow, what you have suggested is not only unsafe, I don't believe it can be done. Your 120V contractors saw has a 3 wire cord and the dryer cord is 4 wire, at least the newer ones are. The only thing I would suggest to anyone is get an electrican, tell him what you want. If it were me I would spec out a new sub panel located in the garage, depending on the main panel's rating ie 100 Amp or more. (Mine panel is a 200 Amp and I will go with a 50-70amp sub panel.) I would spec out all 120v/20amp or 220v/20 or 30 amp depending on the needs of your shop. You could go 15amp for lights but why not 20 amp. I would want 2 ceiling lighting circuts 15 or 20amp, at least 4 to 6 shop circuts all 120v/20amp. I would require that no adjacent recepticales be on the same circut. Next 220 v20 to 30amp I would go with 20amp, one on each wall. That is mostly how my shop is wired except for the aux panel and the 220/20amp circutc and those will be going in during the next few months.
Figure out what your needs and wants are, get an electrican, lisenced of course, and do it the right, safe way. BTW you should be able to ask around and get someone at a reasonable price these days. Be safe, have fun!!!
Wisdom: Where experience and knowledge combine and become one.
"We are all one decision away from Stupid!!"
"How often we sacrifice the permanent plans of God on the altar of immediate solutions"
I have a very good memory, just short is all.