The typical concern for operation on only one engine is that the dripless seal requires pressurized raw water for cooling that doesn't exist when that engine is not operating.
The common solution is for a crossover connection to supply both dripless seals from a single operating engine.
My 2000 380DA was built w/o that crossover connection. When I replaced the dripless seals I installed new parts having the additional port for the crossover connection, then plumbed that properly.
Note that the BIG concern is to ensure / verify that raw water WON'T fill the lift muffler, then back up into the engine.
On my boat there is sufficient elevation between the parts such that raw water will discharge instead of backing up into the non operating engine.
Note that if the boat does not have a crossover connection, then it seems possible to disconnect the dripless seal hose, permitting backwards raw water flow to cool the seal, depending on the bilge pump to discharge that raw water intrusion.
The other option would be to yank the disabled engine propeller.
The last option would be to proceed slowly and hope that the friction is insufficient to damage the dripless seal and the shaft.