That subpanel can't handle any 240V loads, no need to do a load calculation. That's a lot of circuits for 60A.Do you think a 40 or even 30a NEMA would still be too much on the subpanel though?
So yes, your only option is to run a circuit from the main panel. I would strongly recommend hard wiring a Wall Connector instead of a receptacle/GFCI breaker. It is more robust, fewer points of failure. For future proof reasons, have him run a 60A circuit (tell him to use 6/2 MC cable, or else he will likely use non-code compliant 6/2 NM-B/Romex).
Alternatively, buy a Mobile Connector, 50A GFCI breaker and high quality NEMA 14-50 receptacle (where the electrician can use 6/3 NM-B/Romex).