I'm so sorry you've just discovered this. It must be really painful. I hope you've got friends and family round to give you lots of support. 
I've never been cheated on (to my knowledge), so I could be talking out of my backside and anything I have to say is obviously just an opinion anyway rather than established fact. But I have had the experience of dealing with liars or people who twist reality to their own ends.
I would say that the first step in healing is to realise that you don't need to hear the truth. You have more than enough evidence and your feelings to go on. After 21 years and an obvious desire to want to receive a plausible explanation from him, why on earth wouldn't you trust your instincts? Nothing he has said is remotely plausible. 
If he was the sort of person capable of total upfront honesty at this point, he probably wouldn't be the sort of person capable of cheating on you in the first place.
I'm not trying to say that your whole marriage is a sham, because IME he probably does love you and your shared memories of good times are real ones. Like many cheaters, however, he is capable of compartmentalising his behaviour and adopting a selfish and distorted view of reality that allows him to be a loving husband one the one hand and a cheater on the other without there being any sort of conflict in his head.
In his mind it's probably the case that because they are paid sex workers it doesn't count as cheating because there is no emotional involvement. (If he says that BTW you can counter with the fact that treating women as casual sex objects in an industry where women are routinely raped and exploited makes it even worse, not better). He has probably convinced himself that this is just a harmless recreational activity that has no bearing on your relationship and therefore you don't need to know in much the same way as many people keep little 'harmless' 
secrets from their partners. He will probably stick to this line to the bitter end because as long as he denies it, that is the truth as far as you're concerned - you don't need to know the truth because it's his perspective that's relevant here in his opinion.
You need to accept that you will probably never get full disclosure unless he realises that full and total honesty is the only way he can possibly salvage things. Right now he feels that blustering his way out, or only admitting to what you already know, is his best bet. That might never change TBH.
Knowing that, how do you feel?
It's easy for me to say because I'm not the one going through it, but in your shoes I would kick him out and tell him not to come back until he credits you with the intelligence and respect to hear the truth so that you can work out a plan to move forwards (even if that's divorce) like grownups. Nothing like loss to focus people's minds.
Hope you feel better soon.