I attended a pidyon petter chamor in Pittsburgh in 2017. It was organized by the Kollel and attended by many of the local Orthodox rabbis (and lots of other people). Unfortunately the web site they set up at the time is no longer there (and not in the Wayback Machine), but I have a video (linked on my blog post about the event).
In the (first, introductory) video, Rabbi Avrohom Weisswasser reported the research they did, but unfortunately didn't cite a source:
He has the halachos of a holy animal. We're not allowed to work him until after the redemption. We're not allowed to play with him, unless we're doing it for his good. And we were told -- there's a dispute about this, but we were told we can't even dress him up, besides a blanket. (0:21-0:50)
A little later (1:27) he says he consulted Rabbi Ariel Shoshan of Scottsdale, AZ, who had done this mitzvah previously. Whether R' Shoshan is the source of the information quoted above, I do not know.
In the video, during the introductory comments, you can see many children gathered around the donkey, but they're not petting him -- the handler is keeping him away from them. (After, the handler allowed plenty of petting.)
Before the event I had some questions about the logistics of the kinyan (they were selling shares of the donkey so that more people could participate), and they also mentioned consulting Rabbi Shlomo Miller of Toronto.