There are a number of ways to go about this, but the .22 rimfire barrel makes a poor choice for a rechamber to Hornet. The twist is wrong for the higher velocity Hornet round, so a rebarrel would be in order. I had a Martini that was fitted with a .22 rimfire barrel rechambere to Hornet, and I couldn't get any accuracy from it, without downloading it too low.
A better choice would be to get a Cadet centerfire gun, and have it rebarreled with a .22 barrel, with the correct twist. This would also probably be about the same cost as rechambering, and reworking the rimfire block, and extractor.