I guess it depends on your goals. If this is just for yourself, the solution you are using now sounds just fine, use Alacritty as the GUI.
If you want to package it as an app all wrapped up in a single binary that you might want to distribute to other people, you could just write a simple C program that imports both FZF and a tiny terminal emulator like ST (the Suckless Terminal), and configure ST in the C program to launch FZF with your unique FZF config, instead of launching /bin/sh. You could even dump your configs as constant strings into your C program so you don’t need any external config files.