I've done a bunch of tuna trips in my Tomcat but never went in my my 22. There are a number of considerations:
fuel capacity/range/distance to the tuna, ice capacity, wind/waves, and experience/judgement of the skipper. I'll discuss each turn.
1) The primary limitation on the 22 is fuel. My (older 22) had only 40 gals of fuel, while the new ones hold 50. Depending on port and time of season, recreational caught tuna can be anywhere from 20 to 80 miles offshore. Early in the season the tuna tend to be farther out and, of course it varies from year-to-year. On the WA coast, tuna can be accessed from Neah Bay, La Push, Westport or Ilwaco. For the two northernmost ports, a typical late season run might be 45-50 miles out. For the two southernmost ports - 35 miles out is typical. These are average distances in mid Aug- Sept. Some years, they are rarely this close and some years they are closer.
If we assume 35 miles out and 35 miles back + 6-8 hours of trolling at 6MPH, the round trip is 35+35+(36 to 48) = 106-118 miles. In a 22, a good rule of thumb for safety sake is to assume 3MPG. With 50 gals of fuel, that's a total of 150 miles, and using the 1/3 out and 1/3 back + 1/3 in reserve, that would allow a 100 mile round trip with 1/3 left in reserve. So from a fuel capacity perspective, the 22 is marginal. However, it can be done - either by trolling for a little less time or by carrying an extra 5-10 gals of fuel in jerry cans. Note that transferring fuel in jerry cans on rough seas can be a challenge.
Another important consideration is how the fuel is plumbed - especially if you have twins. Sometimes twins are plumbed so that each engine draws off its own tank. When plumbed that way, if one engine fails, you may not have access to half your fuel. So in such a case, your reserve fuel is cut in half AND you typically cannot get on plane on a single engine. So now your return trip is either REALLY long (at hull speed) OR very fuel inefficient (at 10-12kts pushing a big bow wake) and then fuel capacity can become a huge issue.
2) Ice - to treat your fish well, it's important to ice them down in a slurry of salt water and ice first and transfer them to ice after about an hour. Tuna are warm blooded and come in at a temp about 25F above water temperature after a good fight. So figure about 10lbs of ice/fish. A reasonable trip would be 10 fish (some people catch many more, some fewer) so figure on at least 100# of ice in either kill bags or 120-150qt coolers. That's doable but the boat will be heavily loaded, especially if you take extra fuel. I'd limit my trip to no more than 3 total crew on board (including the skipper). One to drive, one to reel and one to net/gaff.
3) The 22 is a very capable boat but you can beat the hell out of yourself and the crew in anything but fairly smooth seas. For such long distances, you need fairly smooth seas in order to get out to the fish in 2-3 hours or less. Those days do happen but they are not common occurrences so you need to be able to adjust your schedule to go out when those days come around. Forecasting is pretty good these days so if there are 3 smooth days predicted in a row you can ALMOST count on the middle day being smooth (but of course there are exceptions). A 22 will really limit the number of days that are suitable - maybe to just a few a year.
4) Experience/judgement of the skipper is another key limitation. Usually, the people asking these questions have pretty limited experience in the ocean and that appears to be the case with you. With the right experience, on the right day, a tuna trip on a 22 C-Dory is very doable. Without the right experience, it's ill advised. Experience teaches you a lot that cannot be easily conveyed over the internet. With experience, you will have crossed the Ilwaco or Westport bar dozens of times and you'll have a good mental image of what the bar looks like for a given set of stated conditions. You'll also learn how quickly it can change and learn to be able to predict roughly what it will look like as the currents change over the day. By going across in less than perfect conditions (not BAD conditions) you'll learn how the boat handles in waves and you'll learn how to ride the back side of a wave in and what happens when you go over the top to quickly and stuff the bow into the next wave. It's best to learn these in conditions that are not perfect but not BAD. That way you are better prepared for when the conditions are a bit worse.
With experience, you'll learn about how much wind waves you can handle and how much swell you can handle at a given period. You'll probably be surprised to learn that a CD-22 can handle VERY large swells as long as they are widely spaced. I had my 22 in 8-10 swells when the period was 20s and it was entirely safe (sea sickness inducing but safe). With experience you'll learn where the crab pots are thick and to avoid these areas in seas that make it hard to spot them. With experience, you'll learn how weight distribution effects the handling and how important it is to strap down heavy objects (like large coolers filled with ice and fish) to prevent sudden changes in weight distribution. Etc. etc. etc. In sum, there's a lot you learn by experience much of which involves being able to correlate reported conditions with a mental image of what the seas are doing.
So in sum, it's doable, but only on the right days and with the right experience. There are better boats for tuna trips.