I had read that they asphyxiated, too. They had to use oil lamps to see what they were doing. That, and no outside air coming in is an easy way to suffocate.
Hunley actually had a basic snorkel system (two pipes thad could be rotated vertical, positioned behind the conning tower). But these could only be used if the sub was just below the waters surface.
Based on the presumed attack profile, the snorkel could have been used. I can’t recall (after three visits to the conservation center in Charleston over the years) whether the snorkel pipes were raised or not when the Hunley was found.