I've used MEK with pretty good results. Put some on a rag then wipe the are you want to clean. Let it sit a bit then hit it again with a little more MEK and use a plastic scraper or a rag and wipe off the residue. Working in areas of about a foot square is the most I would try at one time.
What worked for me was using a razor blade on a holder, the kind that has a handle. That got the bulk of it off. I then went over it with an orbital sander with 40 grit discs.
Nautolex vinyl won't stay on your sidewall with just glue, it'll have to be fastened mechanically and glued. All of the exposed edges and butt joints will curl over a period of time.
Xylene, like WOG said " Wear mask, gloves, eye protection." It is nasty stuff, but will make the job very easy. We used it on a friends Bayliner, prepping it for new carpet. Worked very well, but it is very potent.
I used the Klean Strip adhesive remover. Paint it on wait 10 minutes scrape it off..
Don't let it get on any surface you don't want stripped..
Wear gloves for sure and use outside..