A fused Kyurem maintains its own moveset; whatever moves Reshiram or Zekrom has are irrelevant. The only snags are in dealing with the way it acquires the new moves exclusive to the fused forms. As I phrased it when writing for Bulbapedia:
When Kyurem becomes fused or separated with either Reshiram or Zekrom while it knows certain moves, Kyurem's moveset will automatically be updated without prompting the player. Fusing Kyurem will replace Scary Face with either Fusion Bolt or Fusion Flare, and replace Glaciate with either Freeze Shock or Ice Burn, if one or both of these moves are present. Unfusing Kyurem will perform the inverse of these move transformations. In Generation VIII, it is possible for Kyurem to learn Scary Face by TM after becoming fused; starting in these games, if Kyurem becomes unfused while it knows both Scary Face and the fusion move, Scary Face will be deleted before the fusion move changes back to Scary Face.
If Kyurem doesn't have either of those moves when you fuse it, its moves won't change, but you can still change your mind and get the fusion move back later by going to the move relearner. It is not possible for Kyurem to keep Glaciate while in a fused form, nor can it have the fusion moves or charge moves in its base form.
Other form-change procedures with special moves involved have failsafes to prevent being left with no moves; for example if you take Rotom out of its washing machine after deleting all moves except Hydro Pump, Hydro Pump gets deleted but Thunder Shock gets added specifically to prevent having an empty moveset. Kyurem's transformations here are careful to always add back a move for every move that gets deleted, so there's never a risk of being left with no moves, nor a basic "default" move that the game would need to keep on tap just in case.