Soldering Stainless Steel is very problematic. You have to have the right solder, the right flux and the right heat and even then it isn't a very easy process.
Considering the most common failure mode I've seen is the wire breaking where it flexes at the solder/crimp point. The shrink wrap acting as a strain relief is probably the best thing you can do to extend the life of LPR clips whether they are crimped SST or soldered copper.
I watched a YouTube video on how to crimp alligator clips. The method the guy used worked great. Strip the end of the lead, fold the wire back over onto the insulation, insert into the back of the alligator clip (like the one Thomas shows in his post) until the wire is all inside and then crimp. I assume the crimped area will eventually come loose, but the alligator clip will almost certainly be destroyed by then. Just cut off the old clip and replace with a new clip.