I use RetroX, but you have to pay to unlock the full version after 5 days, it's about $12. The only reason I use it is because it has all of the emulators included, so no need for separate apps. I use it on a Shield and a 2nd gen Firestick, so I assume it would work ok on the 4k one. Plays PS1 games fine, along with all the usual ones.
I did try others like RetroArch & Hyperspin which are free, but I just don't have the time or patience to be doing all the required setup for them.