In short, the way you avoid paying UPS their fee is by performing the customs clearing process they normally provide for that fee. It is fairly simple to do but there are a few prerequisites:
1. The shipment must be personal (purchased for your personal or home use and not for your business or resale), it must be valued at less than $1600 and it must not be a product or item that is covered under some kind of restriction or specific legislation regarding importation. If you are unsure if your shipment is acceptable, check the CBSA website or call the CBSA office.
2. The cost of getting yourself to a Canadian Border Services Office must be less than the brokerage fee you are trying to avoid. As far as I can tell, the importer (you) or their legal representative must perform the process themselves, in person, at a CBSA office. Click here to see if one is nearby. If you find one nearby, it's detail page will show a list of services. It must list the service of Inland Customs Office.
3. If you value your time highly, find polite conflict distasteful or need the shipment by a quickly approaching date I would advise sucking it up, allowing UPS to broker the customs process for you and paying the UPS driver the billed amount. While the process is not impossible nor is it particularly difficult, it can be time consuming and requires a fair amount of phoning and politely asserting yourself to UPS agents. Time-wise, assume that once your package gets to the entry port (Richmond/Vancouver in my case), it will be tied up in this process for at least another week.
This blog is not legal advice. It is a diary of my own experience and research. You cannot avoid paying legal duties and taxes on goods imported into Canada. This is not about avoiding taxes or duties. In fact, part of this process is paying them as required directly to a customs agent. This is about avoiding the UPS brokerage fee which is nothing more than a ridiculously large service charge paid directly to UPS for a service you neither asked for nor necessarily require.