I have two model 1 2nd issue and two model 1 3rd issue, and I have fired all of them with no problems using RWS BB caps and CCI CB shorts. Based on noise and recoil, I think the RWS BB caps are not much milder than the CCI rounds. The mildest of all 22 rimfires are the Aguila Colibri rounds, which fire a 20 grain bullet at only 350 fps, but they come with a long rifle case length, which will not fit the model 1. I have had good success with the Aguila's in some other antique revolvers.
Incidentally, if you search the internet for RWS BB caps, you may find them listed as 6 mm. Don't be confused, they are 22's. The 6 mm designation comes from 160 years ago, when it seems that the 5.56 mm measurement that corresponds to .22 cal was rounded off.