Most of the time, a cartridge conversion cylinder will work fine without any major work. It may just need to be "fit in" by working the action a few dozen times.
The two major brands are Howell (formerly R&D) and Kirst. As far as I can tell, Howell/R&D doesn't make a conversion cylinder for the .36 cal. Navy Remington. If that's the case, then your only choice is a Kirst cylinder.
Your .38 Special HBWCs will work just fine. The reason to use hollow based bullets is that the .36 Navy bore is actually .375 inch, .018 inch bigger than a .38 cal. bore, which is actually .357 inch. The hollow base forms a "skirt" that expands and grabs the rifling.
Guy N. LaFrance
Collector of Curios & Relics, Maryland Designated Collector
Maryland Shall Issue, GOA, NRA, SAF, JPFO
Grand Army of the Frontier, National Congress of Old West Shootists