Lakewood Dude:
If we don’t interact with Goyim why do accept services from them? Perhaps you should consider driving your trash to the dump yourself so that there is no interaction between yourself and the sanitation engineer, same goes for the mail ; pick it up yourself from the post office.
If there may be a halachic problem in giving it specifically for Dec. 25th, try marking it “In appreciation for all you’ve done for us this past year” or give it to him a few weeks early.
Anyway the entire Dec 25th holiday has become so unaffiliated with religion in this country (except for those who are really devout). It has become a commercialized marketing campaign. Did you know that the percieved character of Mr. Clause (not the story, his physical features0 was actually a marketing campaign created by Coca-Cola?