Snug does not want to frighten the ladies (as doing so can mean death to a player) but he obviously relishes his "fierce" identity:
Here are the lines that support this claim (5.1.210-216):
(As the Lion):
You, ladies, you, whose gentle hearts do fear
The smallest monstrous mouse that creeps on floor,
May now perchance both quake and tremble here,
When lion rough in wildest rage doth roar.
Then know that I, one Snug the joiner, am
A lion-fell, nor else no lion's dam;
For, if I should as lion come in strife
Into this place, 'twere pity on my life."
(*Note: A "fell" lion is one who is dead.)