As a male, I had the "priveledge" of working as a "waitress" in a gay bar when I was 16 to 21. The money was great and enabled me to buy that Trans Am...
Having NEVER walked in any kind of heel, one of the resident drag queens took me under their wing and coached me on walking in heels.
1. On a step, roll off of the planted foot.
2. When you feel the heel of the foot moving forward come in contact to the ground, transfer weight from planted foot to the ball of the other foot.
You should NEVER put all of your weight on a high heel lest you relish a broken ankle or broken heel.
Use the heel as a guide or trigger for transferring weight.
Also, for some reason, a little twist of the heel inward, (that sexy model walk) actually helps maintain control without helicoptering your arms around. It's sort of a search for the center of gravity for your bottom.
I haven't worn heels in a couple of years now, But I can remember them quite well. If this male can work up to 4 inch heels and maneuver a tray of drinks around, anyone can!
Good Luck!