Reddit mentions of A Soup for the Qan: Chinese Dietary Medicine of the Mongol Era As Seen in Hu Sihui's Yinshan Zhengyao (Sir Henry Wellcome Asian)

I don't have a particularly detailed answer to your question except from some of my inferences reading about Tibetan knowledge - especially the 17th Century which is my primary interest.

(1) The concept of a "paramedic" is probably incredibly foreign in the Himalayas or on the Plateau. Consider that there was no such thing as a standing army (maybe in Songtsen Gampo's time, but certainly no such thing by the time of the Dalai Lamas and the formation of Bhutan) and no sort of specialization of warriors (ex. light cavalry, heavy infantry, etc.) so there would be no "paramedics" either. What medicinal knowledge is on the battlefield is probably homegrown recipes that the men carried from their villages or nomadic routes where it would be transplanted to a battlefield situation. We're talking mostly herbal medicines and it's probably reasonable to consider that more than a few would leave home with some medicines (some effective, and some not) that were reported to heal or make them stronger.

(2) Any more advanced medical knowledge - any advanced knowledge in general - was held by the literate monastic class. Monks (and occasionally nuns) held all of the knowledge in the Himalayas primarily because it was monks who knew how to read. Until the 20th Century, literacy wasn't really thought of as an endeavor that went beyond religion. The word for Tibetan script even means "Dharma sign" (chökey). A quick Amazon search of "Tibetan medicine" reveals a lot of hits, though I can't verify their authenticity since I know very little about medicine, Tibetan or otherwise.

It's reasonable to consider the presence of monks on a battlefield both before (giving blessings of protection) and after (giving both religious blessings and practical skills to help battlefield injuries).

This doesn't fully answer your question, of course, but you might want to start your search with Soundings in Tibetan Medicine. It's apparently more anthropological than historical, but my ex-gf was pretty high on its wealth of information. I regret not looking more into it, though admittedly Tibetan medicine is a bit outside my general line of work, in retrospect it probably could have helped me in the long run. I'll have to take a look at it when I'm at an English library.

Anyway, just looking at the list of "Tibetan medicine" books on Amazon, the rest of the list doesn't look quite as academic, but I'm drawn to this in particular because it seems to have a lot of original documents. The rest of the search page is interesting (many of the books have Tibetan teachers with Westerners to interpret their "technical" training into English prose) but of course it would be hard to verify much of their information. Perhaps cross pollinating might give you a good idea of what was going on. It's reasonable to assume (as it's often claimed) that Tibetan medicine is a fusion of Indian Ayurvedic and Traditional Chinese Medicine. It's reasonable because Tibetan Buddhism is mostly derived from late Indian Vajrayana teachings, but there is significant Chinese influence in Tibet, beginning with Songtsen Gampo's marriage with Princess Wencheng and up to the Present Day (see the 1950 invasion).

(3) Ladakhi Medicine is (AFAIK) different from Tibetan, but related. It may be worth inspecting if you're interested, especially in this time period. From what I remember from Helena Norberg-Hodge's experience in her admittedly not-quite-academic book Ancient Futures Ladakhi doctors are referred to as "amchis" and have developed a special type of medicine all based around the concept of avoiding surgery. Apparently a Ladakhi king lost a wife under the knife and forbid surgery in his grief. Since Ladakhi doctors are forbidden from cutting open the body, they assess a patient's health by taking a series of pulses around the body. I don't know how extensive this practice is across the Himalayas, but it's worth a peek, especially since Ladakh developed interestingly in the 17th Century (along with Bhutan).

(4) There was a significant Mongol presence on the Tibetan Plateau and the Himalayas in the 17th Century. The complex politics of Tibetan power dynamics was largely based around a series of Mongol tribes - the Oirat, the Qoshot, and the Dzungar to name the most prominent - and their various patronizations of this Lama and that King led to their employment as forces to destroy Bhutan (and I'm guessing Ladakh also). So while Tibetans were certainly on the battlefield, it's probably worth considering what the Mongols knew medicinally (since the concept of a "paramedic" was probably also foreign to the Mongols) since there would be a lot of cross-over when fighting with, against, and intermarrying with Tibetans. My preliminary Amazon search for "Mongol medicine" reveals a lot of stuff focused on Chinese medicine: Medieval Chinese Medicine, and A Soup for the Qan seem promising in this respect.

Hope that helps!