the best way to do this, in my opinion, is to blow it through a "HELLO NEIGHBOR" ( a product which is similar to the toilet paper tube with dryer sheets in it). First blow it through the Hello Neighbor (or dryer sheet thing), then blow it DIRECTLY into the fan.

If that fails, just take little hits in the shower , and ghost the hits; hold them in until nothing at all comes out. I'd say a good 30 -50 seconds will do you good , if you can hold ur breath that long.

did u ever think of unscrewing the pipe on the shower head and blowing it into the pipe?

if the toilet is powerful enough, you can also blow your hits down the toilet.