What is the best non-surgical way to widen mouth/lips for a male?

It's difficult to say without the benefit of a formal evaluation. This is my expertise and a huge portion of my practice. Asymmetry is normal and expected. See an expert who does facial shaping with surgical and non surgical methods to get a comprehensive option. Best, Dr. Emer.

The skillfull use of appropriate HA fillers to enhance the vermilion borders of the angles of the mouth, as well as to add body to the angles can help to widen the mouth. You would be wise to consult with a board certified cosmetic dermatologist and best of luck.

Facial aesthetics are primarily based on facial bone structure. This is certainly true for structures like the mouth.
The only non-surgical approach to widening the mouth is to use neurotoxins to weaken the depressor anguli Oris muscle. This will cause the corners of your mouth to come out slightly further when smiling or during animation. It will have little to no affect without facial expression. providers sometimes use that treatment to create a lift to the corners of the mouth. my personal first-hand experience has not shown that it lifts the corner of the mouth but does widen the mouth while smiling.
Best,
Mats Hagstrom MD