The owner doesn't have to be the influencer
If you don't love being on camera, that's fine. Marketing doesn't require it.
Pick the role that fits
Owner on camera works for some. Owner-as-writer, owner-as-systems-builder, owner-as-trainer-of-the-camera-person all work too. There's no one right path.
Pay someone to handle the parts you hate
A part-time content person (often a college student or freelancer) for $300 to $800 a month does a lot more than most owners realize.
Be the source, not the spokesperson
Even if you don't post, the team can. Your job is to feed them good stories, photos, and lessons from the field.
Take your version of this question further
This is one operator-tested angle on the question. Your shop, your size, your trade, and your team change the answer. Ask your specific version inside Ask a Shop Owner to get a response grounded in how owners like you actually handled it.