There are a bunch of other menstrual cup products around the world which don’t have such an overtly feminine name, and which come in different shapes and sizes.
I personally have been using Mooncups for over a decade — I find that having the one product with me during the entire period is so much more convenient — nothing to forget or run out of, nothing to carry. I also use Clue to keep better track of when things are due, and on the first day or two and overnight I’ll add in some fabric pantyliners for extra security.
For the discomfort factor, it’s usually the (un)helpful stalk that’s the problem — I cut mine off entirely, and can easily grab the cup by the tapered tip.
For the mess factor, it does take a bit of practice, but with this particular method I barely ever get anything on my hands. If I’m home, I’ll rinse it briefly in the sink. If I’m out, I’ll wipe it with some toilet paper, then reinsert after wiping myself. About the same level of mess as a non-applicator tampon (which are standard in Australia).