The rules specially allow an exemption from not loading in a hostile sea zone on the turn that you declare war, so loading the transports is no problem.
However, since your opponent wanted to essentially move the transports for non-combat purposes, that’s not going to work. The transports are in a hostile sea zone because of the declaration of war, and so must either move during combat movement or participate in combat with the Russian ships. If the transports move during combat movement, they cannot move again later and cannot unload later.
So, your opponent would essentially have had one of the following situations:
1. Two unloaded transports that moved during combat movement to avoid combat.
2. Two dead transports because they would automatically lose the naval battle in sea zone 113.
3. Two loaded transports in sea zone 115 that could not be unloaded during the non-combat phase (and therefore easy pickings for Russia or the UK).
It would no problem for your opponent to load those transports and use them to amphibiously assault Russian territory though.
You could not scramble for your opponent reinforcing Finland, since his movement into Finland would by definition be during non-combat and therefore would not trigger a scramble. However, as I previously pointed out, he cannot unload his transport during non-combat movement having moved it during combat movement.
Marsh