Tacky to have reception during museum open hours?

Hi all!
I’m exploring options for a 40 person wedding and trying to keep the cost at $8k. I really love my local art museum, but renting the entire venue is very expensive. Also, you don’t actually get access to the exhibits, just the lobbies- which takes all the fun out of it.

However, the museum has a lovely cafe with indoor and outdoor seating that can be rented privately, during business hours while the rest of the museum is open to the public. For $4k I can run two group tours of the museum (20 ppl each), rent the cafe, and serve an in-house catered seated lunch. Or I could leave the group tours out and let guests explore the museum themselves if they wish? There’s a cute church within walking distance to do the ceremony in for $1k. This leaves $3k for dress, floral, etc, which I think is manageable.
Would you find it tacky if you attended a reception at a museum and the public was at the museum (but not in the reception space itself)?