Excel or Access for surgery booking system?

I realize this isn't particularly helpful but Excel or Access alone are not great platforms for what you're trying to accomplish. You will likely continue to run into file lock issues even if you move your solution to MS Access and I have yet to find a good (low maintenance) way to mitigate this without involving a collaborative file sharing solution such as SharePoint.

You didn't describe much in terms of requirements but, based on some assumptions I've made from reading your post, the best cheap solution that comes to mind would be something like Office Online (if available to you) or Google Sheets. Though, since you're dealing with patient data, a free web-based solution may raise some security flags.

If Excel and Access are truly the only platforms available to you then you might look into creating a "Split Database" using MS Access. It's essentially a single central .mdb with multiple other .mdb's (one per user) linked to it. That way, each user can open their own copy (presumably containing a form to update your tables) without locking the primary copy. This is not a great solution as maintenance is tricky and any updates will be a horrible process especially since you've stated your users aren't very tech savvy.