Trev,
Before you get started, do as Alvin mentioned and start 'The Paperwork".
First: What is the wheelbase (front to back) and track (side to side) of the '37? By starting here, you will be able to decide which vehicle will closest fit the existing frame. Remember, wheelbase can be changed fairly easily (shortening is easier than lengthening, but it can still be done), but it is very difficult to change the track of the wheels and tires. Do you want the tires tucked up into the fenders or sitting outside of them?
Once you have the above figured out, decide on how you will drive the finished truck. Remember, S-10's came with I-4's or V-6's. Yes, you can bolt a V-8 into one, but you are adding a lot of work. The reason I mention this is: if you intend on lots of cruising or highway driving, the smaller engine may do you just fine and give you better mileage (and gas will not be getting any less expensive in the future!). You may want a larger engine if you want to 'light them up' on a regular basis.
I seem to recall a problem with the S-10 (or S-15) swap and the radiator in an AD truck, I think the rad has to be leaned back slightly to clear the sheetmetal. I'm sure your '37 is a bit smaller than an AD, so you may have to break out a tape measure and do some more homework.
I know how you feel about the good old "Armstrong Steering" and fully understand why you wish to change.
You will have to do a good bit of homework before starting on this swap.
Have fun!
Lane