I wouldn't exclude exercises, if the muscles get weaker or less use, then they will probably be less able to handle the daily stress of working at a computer station and typing.
I'm a computer programmer, and I'm a frequent swimmer, so that adds up to the same kind of neck and trapezius soreness/knots that you talk about. I try to combat it in two ways that seem to work for me.
Whenever I feel things starting to tense up some, I try to take a minute or two and do stretching. Not on any kind of schedule, but "as needed," though maybe making sure you do some before bed on a regular basis, regardless, might be helpful.
Stiff neck from sitting all day stretches
Another thing that works, for me, is self-massage, particularly targeting trigger/release points where you can feel those muscles knotting up. Quite often these points are where several bands of muscles come together. When it gets really bad, I sometimes ask my teenaged daughter to get behind me on the couch and lean in and attack the trapezius knots with her elbow.
When doing any kind of release or pressure point work, what happens is the muscles initially will contract or spasm, but if you keep the pressure on, you will feel the muscles begin to relax in response to the pressure ("release"). When my daughter gives me the requested elbow treatment, I usually notice it especially when I wake up the next day.
The points that most often need attention, for me are the top of the trapezius or, more often, just to the spine-side near the top of the scapula, which I can feel running up the back of my neck and to the base of the skull, and, when it is bad enough to spasm, can make if feel like someone is squeezing either my eyeball or my inner ear.
Self-Massage tips for myofascial release points
When I can't get a helper for something like that, if the back of the chair is high enough, or the couch is firm enough, I place a tennis ball between my back and the chair or couch (or you can do this lying on the floor), make sure the ball is directly on the sore muscle, and slightly move/rotate my shoulders and back so the ball is massaging that area. Tennis ball is great for this. I'd image an racquetball would be pretty good, too.
