If you pick up Shillelagh using the Magic Initiate feat, you use WIS for attack and damage with it. If you pick up Shillelagh at level 10 through your bard class feature, you use CHA for attack and damage with it.

There are a few options available for valor bards who don't want to take/can't take the feat. One is to use a versatile weapon, switching between 1h and 2h mode as needed. Ostensibly, you could also use your offhand to cast while holding a 2h weapon (like greatsword) provided you do not attack using the weapon that round, for whatever that's worth. You also have access to a number of spells with only verbal component including one cantrip,Vicious Mockery; a heal, Healing Word, a level 1 direct damage, Dissonant Whispers, as well as both Power Word Stund and Power Word Kill. You don't lose much by just sticking to these spells in combat and using your spells with somatic & material components between fights.