Any time you are surface swimming, you should have a reg or snorkel in your mouth. Doing otherwise is asking for trouble.
The other option to using your compass is to turn your head and adjust your path every so often. This way you don't look silly using your compass to swim 100 yards to the boat.
I would look silly using my compass to swim to a boat during a shore dive wouldn't I
Many Howe sound dives are shore entry with minimal surf but longish surface swims to the descent point.
A lot of people lose the snorkel around here after a bit of time in the water. For me it interferes with the long hose. I do use one occasionally but usually when I'm either vintage diving or specifically planning a surface swim in that style (often a shore traverse at the end of a dive where I want to observe the littoral zone). Otherwise, I have not suffered from an oral fixation since quitting smoking.
In terms of cheek welding, I have never seen someone use that style of compass (though I know it well), or that technique UW. Most navigation needs are not that specific and vis limits the practicality of sighting distant reference points. I have found the cardinal points to be the working points for 99% of my dives. Which way in, which way out etc... in low vis. I rarely follow specific bearings (a few exceptions) because veering due to kick discrepancy decreases accuracy anyway.
There are a few shore access dives that we do using specific bearings. In this case I also want to know the depth (usually of a wreck like the VT-100). Then I can follow the bearing to the depth, turn, and follow the depth contour rightward to the wreck. This is because my right leg is stronger and naturally pushes me to the left of the intended bearing. In low vis, following a precise bearing is (practically) next to impossible because you have no reference point to fix on, so you have to anticipate the variance and work it into your plan. If you're good you can go pretty straight by looking at the compass but usually there is a sawtooth effect of variation and correction that can put you out over distance. In 5' vis that may take you right past the intended destination.
If I were teaching someone new how to navigate I would tell them to do a good job but not to put themselves in positions where they need to rely solely on compass/user precision. Either avoid those dives until competency is adequate or accept the lack of accuracy inherent in the tool have a compensatory technique available.
But what are these degrees? Is it a temperature? I'm used to working in Mils