How do I get GS Shrinkit running on a IIgs?

Well, the RTFM answer is here:
http://home.swbell.net/rubywand/Csa2FLUTILS.html#003
But it involves another round of downloading and executing software which you may or may not be interested in doing. You "just" have to change the file type from text to app, but that's tricky without another utility. 🙂

It is a chicken-and-egg situation at first - but once you get a couple of those fundamental tools working, the dominoes start to fall quickly.

That's the biggest quibble I have with the original MacOS/GSOS. The implementation of file types/creator codes has such a strong association with what can "open" a file. It's a double-edged sword. Sure, it keeps you out of trouble because an incompatible app won't be able to touch it. But then sometimes you want an incompatible app to be able to touch it. They tried so hard to keep us from hurting ourselves...

Even on OSX, I have a filetype editor so when I appletalk my files around, they can arrive at the destination in the right shape. Hey, that's another option for you... check out Super Get Info:
http://www.versiontracker.com/dyn/moreinfo/mac/11311

I don't know ShrinkIt or the IIgs, but Mac files with a .sea extension are Self-Extracting-Archive files. They contain a tiny unpacking Application and the software to be unpacked. Double click on them on a Mac, and they unpack themselves into the software you really wanted.