You can bring in several different approaches to creating an improvisation, including a chordwise approach. This means that you entirely can use a given song's chords and not the song's melody, key, or otherwise. In this way, you can exclusively use fill-ins and other musical effects to make an improvisational process. Here is one example (in Chords On Piano 3 page 66-67, there are several more, and even exercises).

Below you can hear an example of an improvisation of bar 9-16 of This Little Light Of Mine. Here we mostly use arpeggios with short and long blue notefill-ins, while the left hand goes triad. Furthermore, tremolo, lift, one grace note fill-in and suspension fill-in. Note the numerous repetitions of small motifs.

This Little Light Of Mine (improvisation)