IMO, i would rather you use the FP's website and pay a fee than be late. Besides, if you happen to be late, they would not only charge you a late fee, they would also report it to the credit bureaus
Only 30-day lates are supposed to be reported to the CBR's. In this case it would be a 1-day or 2-day late. It is, however, not a good idea to be late in any manner with the OC at any time, for any reason!
IME, many CCC's can clear a payment overnight:
These all regularly clear next day when I initiate a payment on their website. So don't assume that it will take 2 days.
OP: If your CC is FP, then the limit is most likely a relatively low CL, meaning your minimum payment due is relatively low. IMO, you need to figure out how to have the money "left over" from previous check or just make the payment with the previous check (assuming you get paid 2x per month). You don't have to wait till the day due to make your payment.
If you end up with NSF you will get hit with fees on both ends for the NSF, plus a LATE fee on FP, etc. And if you are avoiding FP web pays due to fees, I don't see "floating" payments as a good idea.
I would just get the schedule adjusted 2 weeks prior so that you are making the payment on the 1st rather than 15th. And if you are so close check to check that you can't, I recommend selling something or getting another part time job till you get things paid down.
Do you have any emergency cash? If so (and you really should) pay the minimum payment due out of the emergency fund, and when you get the DD pay check, pay the emergency fund back.
The point I am making: you need to get some breathing room, both in time of payment made and in discretionary income and emergency funds.