Would you allow voice as a musical instrument? I think either singing or maybe oratory or storytelling all fit the idea of a bard. I'm happy to take that an instrument proficiency, since the bard class gives 3 of them. The advantage becomes that she doesn't have to drop instrument/weapon to swap to the other one. But there can be a couple of issues with that, namely:
1. What if the bard gets muted, as by a Silence spell?
2. A bard typically uses a musical instrument as their arcane focus. It could either be worked into the lore that somehow her voice IS her arcane focus, or else I can carry an actual physical instrument as the focus/backup focus.