There will be two main issues to deal with:
* The bolt face- head size on the 39mm rounds is smaller than the "standard" head size of .470" (30-06/308 size), so you would have to find a 223 Rem rifle and have a smith rework the bolt. Sounds moderately expensive.
* Bore size- 5.45X39 does not use a standard .224" bullet, it uses a .219" bullet IIRC. This means a custom barrel from someone who is willing to make a one-of-a-kind barrel. Sounds very expensive to me.
Perhaps the best option would be to buy a rifle in 7.62X39 (Rem 798 or CZ)and have it rebarreled to 22 Waldog or 22 PPC, which use the 39mm case but use a .224" bullet. Or just shoot it as a 7.62X39 and enjoy.