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I would be starting from the get-go as well..
Was thinking of pushing on a tool held in-hand.

IF it is controllable!

I think outback mentioned some bolsters...
Anything which pushes should be handy, Randy! (Made a rhyme!)
Not so much into pushing these days. Something to push for me?

Possibilities seem...

OH! Seems like you could change-out the top/bottom dies to smack almost anything?

If it is super-controllable, a flat or concave ram pushing lightly against a leather punch. Make holes. Make...

Leatherwork?

How fast is it? It could be used for pinning! ;)

Seriously, the old collarless peens on the old Gencos, Cases and such always led me to think they were done by such a tool. Maybe some hollow...