The way my group has always ruled it is this: you cannot sheathe a weapon and draw a new one as part of a move. You can, however drop a weapon and draw a new one as part of a move, with whatever negative consequences that entails.

Does it take an action to sheathe a weapon?

Unfortunately, it would require your action. You can sheath a weapon or draw a weapon using your free object interaction, but not both.

Can you sheathe a sword?

verb (used with object), sheathed, sheath·ing. to put (a sword, dagger, etc.) ... to plunge (a sword, dagger, etc.) in something as if in a sheath.