I don't subscribe to the notion that gun topic writers know all the answers to all the questions. That said there is an article in number 209 of the Handloader Magazine about just what you have asked. The article was pinned by Ross Seyfried, and he states he uses small pistol primers in at least some of his 22 Hornet loads. I believe it to be safe to use pistol primers in the 22 Hornet at the pressure it works in. Most of the loads for the Hornet are in the low 40's and a 357 Mag also operates in the low 40,000 CUP. I also believe Lil'gun powder needs a rifle primer to light it off. I use rifle primers in my 38 super, so much for what the primer box says. Common sense goes a long ways here.
Dan
