I am in FL, so YMMV.
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Generally, it's ok to vax some and then have a change of heart. The problem is going back to vax after having used an exemption. In FL, doing this will cause you to lose your exemption, as both vax records and exemptions are entered into the database. (You can opt out of having your doctor upload your shot records, but you can't opt out of having the school send on your exemption. This is so they can identify unvaxed persons in the event of an epidemic.)
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Don't allow your doctor to release the existing vax records. Specifically forbid it if necessary. In my state, the doctors don't send anything; the parents are responsible for turning in vax/exemption papers and physical records.
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I also choose to opt out of the "requirement" to submit proof of physical. I don't need Big Brother to hold my hand and ensure I care for my children, and I also don't think the school has any business nosing into our protected medical info, although that sort of had to change when my kids were both diagnosed with different chronic medical conditions. We had to provide letters from the doctor in order to get 504 plans.