Yes, surely you can delete it. Here is an example of GeoIP.jl which was recently updated from pre 1.0 to 1.0+ version: https://github.com/JuliaWeb/GeoIP.jl/pull/29/files
I removed REQUIRE, add Project.toml and some CI scripts.
If you doubt about uuid and other things, then the easiest way is to generate new project with the same name with the help of PkgTemplates.jl and just copy all files (except src and README of course) to your old project.
This should work smoothly if it was removed from the Registry. If it is a registered package, you should use it’s current uuid.