You say you "think" you wife is happy with the current arrangement. Don't the two of you communicate at all? You're not telling us why you can't end your marriage, possibly for religious reasons, but as you don't have children presumably nobody put a pistol to your head and forced you to go up the altar when she was pregnant? . Did you ever love her, or has love died simply because the two of you have nothing in common? If you have nothing in common, presumably you married in haste before you gave yourself time to find this out, in which case how can you be sure that your judgement has now improved with this current lady?
I think it's time for you and your wife to sit down and have a very long and honest talk. I think you need to tell her how you feel about her and this other woman and see what her reaction is. If she's starting to talk about wanting children if would absolutely foolhardy of you to contemplate having them in a loveless marriage, so your wife needs to know this too as you'll be condemning her to a miserable existence too if you deprive her.
So it seems to me you have the following options if you want to satisfy your conscience and honour:.
Do nothing, not have an affair and be totally miserable for the rest of your life..
Be honest with your wife, have a discussion and see where this leaves you.
Opt for an honourable separation, continue to see this woman as a friend only and hope your wife will eventually file for divorce if she meets somebody who can give her what she wants.
Time to bite the bullet I'd say !