Hi Hannah! I'd like to congratulate you and your org on your visitation growth. It is clear your space is offering something of value to your patrons, so here is a guest-centric perspective.
The first step is to discover why the 1% are engaging with your artifacts in ways that are undesirable.
*Is it because they are curious? If so, what ways can you position content or interpreters to help satisfy the curiosity and keep the objects safe?
*Is it because they don't know or understand the difference between "touch this and not that"? If so, that is a different problem to solve. In this case you might consider the ways you can use spatial guidelines and/or trained staff and volunteers to help clarify the difference.
I also encourage you to get curious about who is doing the undesirable touching. What are their needs? What opportunities are available?
How do you cue guest behavior in clear, but welcoming ways? Rather than a list of "don't do's," can you have some clear graphic signage of "can do's" and share why its safe to handle that object, but not the rest.
I have much more I can say, but the best place to start is by framing the challenge as an opportunity for a new kind of welcome. Reach out if you want more ideas!