Here's something that a lot of people who grew up playing video games and D&D just don't "get".
There are no "weapon styles" for which any given person is just physically naturally inclined to by some sort of secret statistic written down on their character sheet somewhere. Some people have preferences and some people seem to be naturally inclined, mentally, to certain styles, sure. But there's no way to determine what you'll like or do well with except to have you pick up every style and try it, many times, in many situations, with many teachers.
In the same way, lifting weights is good for every style. If you can crush peoples' sword blocks and demolish lines sword'n'board, good! If you can break shields, literally actually break them, with a 5' red sword, great! If you spear so hard you knock people over with a hit to the center of their tower shield, wonderful!
But it's not like "Oh, you do powerlifting? You should definitely use a 39.8 oz 6'2" flatblade glaive with a stabbing tip and a 27" handle" or "Oh, you focus mostly on plyo and long-distance running? Flail and mace, homie" the same way it's not like "Oh, you have an 18 STR, you should use two-handed weapons cause they benefit from Power Attack more" in real life.
Made me chuckle. Yes I realize you can't pick a weapon I will love, I am apparently phrasing my question badly. Are there any weapons which use under hand blows, pushing, or forward momentum of the body similar to the movements I listed?
You all are better at me at fighting and several have a lot of experience with different weapons (what I called styles) and I wondered if anything utilized these particular movements. Single sword seems to me (and I am probably wrong) that it uses a lot of arm and shoulder strength in the lateral plane and can put a lot of stress on the elbow and wrist (of which I have plenty and don't want to double up).
If there just isn't anything like that, then that is an answer I am looking for.
Add: If Dag is your main hobby and you decide to take up martial arts as a second hobby, but want it to be useful for Dag you would want to find a "style" that worked. So wrestling, judo and possibly ju-jitsu would have some carry over but Muy Thai, karate and boxing, although good for conditioning, would be mostly useless.