Lights

go for UV, for the insta-cancer effect, or Infrared to go for blood boiling

He wanted to melt the face, not zap the DNA or vaporise the blood. While it's surprisingly hard to find the latent heat of fusion for subcutaneous fat, it does seem that you don't need to raise the temperature very much to get it to melt, so latent heat is the key. We know that 1kW/m² of white light is nowhere near enough, otherwise we'd melt in sunlight. The face is about 0.05m², so we definitely need well over 50W to melt the whole thing, and the total power required will depend on the amount of time we are allowed to illuminate the target. There is a danger of simply ablating the surface without melting anything if we go for a very high power for a very short time, but if we try for melting with a low power/long duration pulse, people tend to run away before we can do any harm.

We can burn people with thermal radiation dose of about 100 using this calculation method, which is equivalent to about 30kW/m² sustained for 1s. Even with very good IR optics, we clearly need our emitter to be putting out >1kW to give ourselves a chance of doing some useful damage within the likely target illumination times, but we don't need to turn it on until we have the target in sight, so the battery need not be huge if we only want to zap a few people on each trip, the energy per shot is about 1kJ if we can generate a beam which doesn't fall outside the target area, compared with a total energy storage of about 30kJ for a typical smartphone battery.

TL;DR
You can't literally melt the face of somebody who isn't tied down