You feel ashamed because you feel you violated your marriage? Or, do you feel ashamed because you had did something with another guy? Or both?
I know a LOT of married guys that have kids, love their wives, etc, etc, who also realise there's a large part of them that likes to have physical contact with a man once in a while. They'd never leave their marital situation, but at the same time it gets to a point in their life where the curiosity becomes a need. Its where the part of them (and it comes down to finally recognizing that it IS a part of them) that has been put off to the side for so long comes for the forefront.
The first time is a shocker. You have a ton of thoughts warring with each other. Marriage vs your Inner You. The guys that I know that have decided to maintain their marriage tend to do one of two things: keep finding a series of anonymous people over the years, or they have one or two guys they can trust (usually in a similar situation) that they see whenever schedules allow. Both have pros and cons.
Anonymous lovers keep you firmly in the closet with no one really knowing anything. You get to meet up, have fun, and leave. No commitments, no phone calls, no one knowing where you live, etc. But, they ARE strangers and you never know who you are meeting. STD's are an issue here as well, but you seem to be aware of that and are using protection.
Finding a lover or two can take time, but it can be both safer (you know them, he's not going to tell, he's STD free) and potentially more stressful (emotional involvement, unless carefully managed in front of your spouse, can bring up questions).
Just a couple thoughts anyway. Don't be afraid to talk it out on these forums