Starting to do voice lessons/vocal coaching

Hi! I've been approached by a few potential students who have asked whether I teach voice lessons or provide vocal coaching. I am an experienced singer with a rich theater background, and a good ear for pitch and tone. I currently teach mommy & me classes for little kids and am music directing for some Broadway Jr shows. I am confident that I could help singers improve their technique. What is holding me back from agreeing to be someone's actual voice teacher, though, is my piano skills. I can play... but at a fairly basic level (I used to be decently good but am out of practice). I can plunk through a melody well enough, but can't pick up someone's piece from their book and just accompany them at tempo. Is that a deal breaker? Are there any tips or pointers on how to shape a lesson where I am NOT accompanying? Any apps that can supplement me? It's something I'd really like to do, but not if i'm not going to be good at it. TIA!