Loan Servicing Question: Skipping a payment during a refinance

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Hello all,

I am in the middle of a refinance right now.  For reference, I usually pay my mortgage on the first and was planning to make my payment per usual on May 1st.

Since I am scheduled to close on May 7th and I technically do not have to pay until the 10th, am I okay to schedule my payment on May 10th and basically skip this payment with my old lender once I close on the 7th?  Will this impact anything with my refinance through a different or is this a somewhat normal practice?

I would essentially skip May as I close the new refinance before the grace period is over, then I will also get to skip a payment in June with my new lender.  I would then make my new payment on July 1st.

Any insights?  I sure don't want to screw anything up with my refinance.

Thanks in advance!