I can't speak for ordering from Mouser, nor is my experience current, but in the past I found that UPS only charged brokerage fees on ground shipped packages. Once I found that out, if I had to use UPS, I would always use Next Day Air shipment which resulted in my only having to pay for the actual taxes and or duties. In my case, I was ordering SLR lenses, flash gear, flash meters and the like from New York. The cost turned out to be about the same for next day air with no brokerage fees vs regular ground shipping with all the so called fees added on. At least with Next Day Air, UPS has to give me decent shipping services for my money.
Now, as for Mouser.... I would give them a call or catch someone on the live chat service they offer during business hours. I'm quite sure they have some sort of arrangement similar to Digikey which is also based in the US and ships via UPS without dinging the customer with brokerage charges. They may be set up as a non-resident importer and may charge GST/PST on your order up front so the package simply arrives at your door without hassle.
Well, it wouldn't hurt to ask, anyway.
Regards
Christian