There is absolutely no reason to take a 20 year old car to a dealer’s service department.
However, I would avoid places like Pep Boys and Sears (and other chain-run establishments) like the plague.
Any trained mechanic can work on a 20 year old Toyota, and a mechanic at an independent shop will more than likely do it with more competence and at a much lower cost than any of those “chain” shops.
All of that being said, high HC emissions are usually the result of lax maintenance. So, replacing spark plugs and air filters that are over-aged will frequently do the trick. Sometimes it is necessary to do additional work, such as replacing spark plug wires, or adjusting the ignition timing (if it is actually adjustable on your engine), or cleaning the EGR valve, but none of that requires a visit to a dealership.
However, it is also possible that excessive engine wear is the cause of your high HC emissions, and if this turns out to be the case, then you would probably be better-off getting a newer car, rather than spending the money to overhaul that 20 year old engine.
Just for the sake of discussion…
How many miles are on the odometer?
When were the spark plugs last replaced?
How often do you change the oil?
How much oil do you need to add between oil changes?