Can the bladesinger fight without magic?

My wizard was captured by an Erinyes and confined in an anti-magic zone. I can pick the lock and escape the prison, but I may end up having to fight 1d3 succubi plus 1 of their quasit familiars. My AC is 17 since I have an elven chain mail, but I can't use spells, and I think the bladesinger doesn't work. On the other hand, the succubi can't use their magic abilities either, so it will be a melee fight. Should I wait for the group, or do I have any hope of defeating at least one succubus?