A perpetual swap is just a contract-for-difference. Assuming the basis for bitcoin is solely driven by interest rate differentials (spoiler alert: it is not) then the total cost of carry of holding a cfd on bitcoin and holding a tailed future on bitcoin would be the same. The carry costs are just explicit with the future and implicit with the cfd.
This is just like any other option. For example, if you are trading an IBM option, you hedge with IBM stock, which doesn't expire at all, (obviously).
You then sell your hedge in the gamma-storm that enuses at expiry.
For longer term options where you have an expiry that goes way past the futures you have two choices:
Trade the rolls periodically