I think a mission like this would be a good alternative to sub vs sub

This is a brilliant idea, and could rely on basically the same logic as the artifact recovery missions. Difference being the "artifact" starts on Team A's sub, while Team B has receive it/make the actual delivery.

Only challenge is giving the Team A in the above scenario something to do after the transfer. One idea is Team A can start in shuttle and needs rescue/pickup of critical cargo. This would add a bit of time sensitivity and make it logical for crews to merge & complete the second half of the mission.

Hey, that's a good idea. But some of the cargo we have as cargo missions today, can't be taken outside. These cargo can be nitroglycerin, C4 and Compound N.
As nitroglycerin blows up when pressurised, the C4 and Compound N will degrade when in contact with water. That will become a bit of a problem. BTE has it sorted out though, with diving chests that are waterproof and pressure resistant.