Hi Philip
As i said, rimfire for sure. For a start, the protuberance in the hammer is not a punction pin, but a "I" trace, to smash the cartridge rim. Surely both pistols are to fit a short cartridge, due to the small space available when the hammer is cocked. No doubt they were made to fit a .22 short, or the like. I would not stand an academical confrontation on the priest version, as it was verbaly transmited by an antiquarian ( or two ? ). The cyclist version is more popular. But remember that, in the beginning, the purpose was only to scare the dogs ( more proper for priests ). Also you find in this type of calibers buletless cartridges ( alarm fire ) with only the blowing efect.
One gets lost in the countless versions of small calibers, let me tell you. I do know about the 5,5 center fire velodog, used by Galand. But what i actually have is a center fire six shooting hamerless revolver, clearly marked 6 m/m velodog. Indeed the velodog cartridge is longer than the vulgar .22 LR. Its a very plane piece but, if need, i can post pictures. It is numbered, but without maker's mark.
This is a french link on small pistols, with some examples similar to mine
http://site.voila.fr/collectionarme/miniature.htm