There was lots and lots of White naval units, and they did fight. Just not at sea.
The Reds took all the Petrograd fleet. They skirmished a bit with the British and Estonians, but no Whites.
The Whites took most of the Black Sea fleet. Because the Allied powers were present with powerful fleets, the Reds couldn't really fight seriously there.
The Caspian did have some naval encounters. Various patched together naval forces, mostly improvised.
Meanwhile every major river pretty much had a White flotilla and a Red flotilla. The big Russian rivers are BIG, and allow for quite a lot of manouevre.
The flotillas supported the land operations, and fought the opposing side's flotillas as well. There's actually quite a lot of information about it. But sadly almost all in Russian.
It would have to be a labour of love, to convert the various river boats, but they did fight.
opens the box on a Battlefield in a Box house.
