I just like the word "migi" better than "hidari", and being right handed makes me connect that easily. Migi just feels right (pun intended)
For remembering the Kanji, I have one silly tip (based on traditions from India (I think?)):
Migi - Right - 右 - You put your right hand to your mouth 口 when you eat.
Hidari - Left - 左 - You use your left hand to clean your butt (and エ almost looks like a butt crack).
I know it's silly, but it sticks!