The non-explodey solution is most likely going to require *both* sending enough money to Houthi leadership to save face, plus turning up with enough muscle to ensure an agreement to remove the oil is honoured.
The US military has never been a force for good, nor a force for evil either. The US military, like all other militaries, is a force for its own country's purposes and goals only. The rest is propaganda.
History has put the US in such a position this propaganda, and the area of control of its military, is extremely widespread.
Of course, and for everyone but contrarians, sometimes the US has goals that are a net good. Sometimes the US doesn't, and sometimes the US uses the military inappropriately for commendable but open-ended goals. This isn't open-ended, and not having the tanker is a net good, and you'll notice I emphatically did not suggest using only the US military. I suggested the US military provide security for whatever deal is struck.
Assuming we're living in reality, what non-force-backed solution do you propose that doesn't end with "Thankyou for $ASSET. There has been problem. Send more $ASSET."... Forever?