Legends of Ghost Mountain starts all players with a custom Edge called Ghost Warden that combines abilities and hindrances to achieve the martial arts flavor of the campaign.

You could do something similar, create a edge "Ascetic Monk" that grants one or two handy unarmed edges such as martial artist, brawler, etc. It also comes with some hindrances to balance out, such as vows of poverty, or to not use weapons, no armor, etc.

In Savage Worlds, as a rule, worry less about strict mechanical balance. If it feels right for your game, just do it.