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Hello,
I hosted an open mic for about a year. If the venue is even reasonably equipped, they will mic your guitar into whatever sound system they are providing.nit is a good technique to contact the open mic host and confirm this ahead of time.
There is a good clip on mic you can buy from a small North Carolina company, Bartlett Audio. I have one that I move from instrument to instrument as required.
https://www.bartlettaudio.com/ I have the one with a power supply that connects via 1/4 jack to an amp/pa or mixing board. You can also get an unpowered option with an xlr (3 pin). I would bet any host can work with either.
Open mics are great non threatening fun.