far-trader
SOC-14 10K
Don't forget that CT also encourages refs to add new skills as the need arises. That would seem the more appropriate step for your wants. But I'm not really sure it's needed the way the Wounding and Death rules (Book1 p33) work. It looks more like your PCs need to recruit a Medic 
But something like First-Aid might be a good addition. Where First-Aid-0 would be the basic course taken by ordinary people and never used. First-Aid-1 would be instructor level, lots of practice but no actual. First-Aid-2 and higher would be some use of the skill in actual practice. Allowing First-Aid-0 for ex-services personnel wouldn't be unbalancing with the following rule change:
Or something like that
I don't think Medical-0 is appropriate. Medical-1 and Medical-2 are steps in the Bachelor Degree, pre-Med if you will for those with higher final skill level. Or full Nurse, Emergency Responder, or Field Medic for those who's skill goes no higher. Medical-3 is the full MD and Internship while higher levels are simply talent and/or experience.

But something like First-Aid might be a good addition. Where First-Aid-0 would be the basic course taken by ordinary people and never used. First-Aid-1 would be instructor level, lots of practice but no actual. First-Aid-2 and higher would be some use of the skill in actual practice. Allowing First-Aid-0 for ex-services personnel wouldn't be unbalancing with the following rule change:
Wounding and Death:
Unconscious wounded characters (one stat at zero) recover consciousness after 4 combat turns of successful First-Aid. Roll 8+ with DM = First-Aid or Medical skill level. If unsuccessful or not treated they recover consciousness in 40 combat turns.
Unconscious seriously wounded characters (two stats at zero) must be treated within 1 hour, the Golden Hour. They recover consciousness after 20 minutes of successful First-Aid. Roll 10+ with DM = First-Aid or Medical skill level. If unsuccessful recovery requires 3 hours. Untreated wounded characters will die from the trauma at the end of the Golden Hour.
Dying characters (three stats at zero) must be treated within 10 minutes. Roll 12+ with DM = First-Aid or Medical skill level. Success saves the character but they remain unconscious and must be treated by Medical-3 in a hospital within the Golden Hour to recover to a seriously wounded state or they die.
Note - Installation of the character in a charged lowberth will extend the Golden Hour.
Or something like that

I don't think Medical-0 is appropriate. Medical-1 and Medical-2 are steps in the Bachelor Degree, pre-Med if you will for those with higher final skill level. Or full Nurse, Emergency Responder, or Field Medic for those who's skill goes no higher. Medical-3 is the full MD and Internship while higher levels are simply talent and/or experience.