Adding to Ann's answer, Lauren, a tactful (tactical?) attempt at convincing the difficult uncle to take a yDNA test at Family Tree DNA may be worthwhile for a second reason: they're the only major lab that stores the DNA sample to make it available for future testing. Their procedure is actually for the tester to provide two cheek-swabs inside two separate vials. If the first sample opened is viable, the second vial goes into long-term storage, but even the opened vial can be used repeatedly. My first test with them was in 2004. I checked recently, and an upgrade I ordered last month was the 16th individual test applied to that almost-14-year-old sample.
Mileage will vary, of course. Broad-scale, NextGen tests like the Big Y require more original material than the standard autosomal, yDNA, or mtDNA tests, so a new sample may be required for that unless the long-term vial is still undisturbed in storage. Too, if the first vial tried for the initial test contains a poor or inadequate sample, the lab will open vial number two to complete the test (the message there is SRRT: Swab Really, Really Thoroughly to make certain you have two very viable vials).
Our aging ancestors and close relatives won't be around forever. For genealogy--particularly in terms of autosomal results--getting their DNA tested is important because it puts us, generationally, closer to the ancestral connections we're researching. A test at FTDNA is sort of like a biological time capsule. A low-cost Family Finder autosomal test today ($59 right now), and that sample goes on file, allowing you to go back two, three, a half-dozen years from now and order a subsequent test.