Interestingly specific question for asklemmy :D and as someone else said: always ask your vet. But hoben the nature of feline asthma, hearing of other ways different vets tried to tackle this with can be helpful.

Our cat is currently on systemic prednisolone via pills. I don’t know the dosage off the bat - they can be split into quarters. The vet told us to gradually reduce the amount by one quarter every two weeks as long as the cat has no asthma-attacks.

When we’re down to one quarter, we will try to switch to the inhaler and see how that goes.

Two things to keep in mind with feline asthma: a) it takes a long time for the levels to adjust and thus see correct effects and b) there are so so many different dependencies like stress, food and other infections. Our cat is prone for UTIs. As soon as the bladder makes problems, we are up again with 1 whole pill per day and she will still get asthma-attacks.

So also watch out for other conditions, they may interfere.