OK to answer your question about using a 30 amp fuse, if you have a direct short the 30 amp will also blow. AS far as hurting the compressor, the compressor will only draw what it draws, supplying the compressor with extra amp capability will NOT increase what it draws. Before you go 30 amp, how about trying a 25 amp?
Now, the only possible potential damage will be to the battery itself. If you are using the stock lead acid battery it will eventually be weakened from hitting the horn. The drop you saw is about right, so you can imagine what continuous usage is doing something to the battery. I highly recommend using an AGM battery which can handle a stronger load with ease...