answering your question, I'd normally use GNU parallel to orchestrate shell commands over multiple files. to skip already-converted files, I'd just add a conditional to the parallel command, something like:

parallel < input-list --gnu -j<N> test -f {.}.<ext> '||' <convert> {}

the {} notation saves a lot of trouble with whitespace quoting as well

and if you have the files as an argument list rather than in a file, use ::: "$@" at the end instead of < file