No, since the plans are the same and the financial results would be the same, you may choose which meets your insurance needs the best.
Like you say, the health insurance premiums would be deductible on your Schedule C if you pay for your own insurance.
A great resource for you.
https://www.irs.gov/businesses/small-businesses-self-employed/self-employed-individuals-tax-center
Hope you find this information helpful!
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