Can a S&W 38 be shot in a 38 special?

To me shooting a .38 SW in a .38 Special would be ill advised. The .38SW is a little wider (.360-.361). However, the current Remington .38SW LRN 148gr measures .358 suggesting a fit. I still would not take this course.

How effective a round is it?

Depends on your application. .38SW has been described as accurate and light recoil and low report for target use. Having shot .38SW in a vintage Webley, the Remington load was very "light". So light that I would be hesitant to use this factory load for personal defence. As mentioned above, factory loads are prepared with older .38SW pistols in mind. When the cartridge was popular there were many, many manufacturers and models available with materials and quality in wide variation.

Is it as accurate?
.38SWs have been described as accurate. My Webley .38 4 inch produced a 3 inch group at 7 meters with factory load. I'll be reloading, with the correct size dies and materials and will expect improved results.

Can S&W 38 be found, and is it reasonable priced?
Depends on your budget figure $100-$500. Check the auction sites like Gunbroker. Don't scrimp.

Does it have more/less recoil as a 32 magnum?
Unknown, I've never fired a .32 magnum.

I have really bad hands, 38 special is too hot.
Consider reloading your .38 special or purchase custom loads that are "loaded down".
If your hands are infirmed, why not trade your .38 in for a .22 or .22 Magnum for target work. If personal defense is an issue look for a .22 that resembles a larger relative. (e.g. Stoeger or Erma luger in .22), many Smith and Wesson large calibers have .22 cousins.

Hope it helps.