A mild oath that starts with "e" is usually "egad." Perhaps the "m" is incorrect.
Dang?
Calm, mild, cool, soft.
lull, mild.
Heck.
drat
drat
heck
drat
Four letter mild oath starting with h= heck
Some four letter words starting with M are, made, make, mint, male, mail, mill, mall, maul, mule, move, more, moon, moot, mate, meet, moor, mile...
There is verse in Matthew chapter 5 that starts gently Jesus meek and mild.
Mild