With 22 years, even though it is a shipyard and not a commercial nuke, you should have no problem. Figure out where you want to go, and either contact the utility through it's web site or, if you want to go as a contractor, find out who has the contract and call them. If you have no real preference where you want to go, you can get a copy of the outage list from this site, plan a schedule and contact the staffing company. Alternatey, go to Bartlett's (or DeNuke's, or ...) website and look at what is available. Bartlett has the lion's share of the contracts and a very long discussion of the company can be found in this Forum.
One word of warning... your timing is particularly bad right now, this being the end of the outage season. Next fall may be the earliest you would get any kind of selection to choose from... unless you want to go with the other option of DOE or decomissioning or DOD cleanups which run all year. Each option carries a unique set of qualifications, most of which you should not have a lot of problems with. It is just a matter of which route you want to go and which tests you want to take. Read the posts on this forum for details.
Good luck and welcome to NukeWorker.com!