Tbh I don't think a 2nd weapon for Medic (which I would love) should be
more powerful par se, just different in function. Since Medic is not supposed to be as powerful as the other perks in damage output, it would be a 2nd rate rifle, or 2nd rate melee weapon, just like the MP7 is a 2nd rate AR (yes I know it's an SMG, but looking at it purely from a "It's a player armament that produces hitscan attacks that do X damage with X spread" gameplay perspective it's a 2nd rate version of a Commando weapon).
However, it makes up for being 2nd rate by also being light in weight and also having a healing attachment. So if you were a typically Commando player going Medic, the MP7 would be a comfortable weapon for you. But what if you play Support? Sharpshooter?
Hence, I believe that Medic should simply get different tier-1 weapons that mirror the other perk's weapons (a small-barrel pump shotgun, a rifle, a light melee weapon) that also have different healing attachments (an AoE healer that uses 100% charge, a more rapid medi-dart shooter that uses 10% charge, a melee weapon that auto-dual-wields the syringe in the off-hand) that allow the Medic to do all of the utility benefits that Jester described (though not as well as the actual perks themselves), while also seamlessly allowing him to be a Medic.
I think it'd be fitting for the Medic's armaments to take a high-tech slant like that, since his benefits (insti-heals, medi-darts) require the greatest suspension-of-disbelief. The Medic is honestly the most unrealistic perk, so it makes sense he would get the unrealistic weapons.