How can I calculate the possible number of correctly formatted version one minikeys?
Because outputs of SHA-256 can be considered equally distributed for the whole space and this property passes for the first one byte of those outputs, you can calculate this number easily with a really good approximation. One in every 256 in the space you mentioned would be a valid minikey. This approximation would be very good, since the space is, as you noted, really large, so it follows the law of large numbers.

If you needed an exact number, however, your assumption would be correct, though, calculating this number would require to check every possible "candidate" minikey in the space, which would essentially be bruteforcing the whole space and won't be computationally feasible.