In my case, I started punting because my wife had lost all interest in sex. Once she actually told me that I should "look elsewhere" for it... and I did. Though I can't just assume that she really would be OK with that, it's best never to make that assumption, just keep it secret.
In any case, there's absolutely no way that she would approve of me paying for it! We are not exactly wealthy. But she never comments about the fact that I've stopped pestering her for sex, she probably assumes I'm shagging some bored housewife.
It's not too difficult to keep it separate from your "real" life. Use a false name, and an unregistered or secondhand mobile phone (or simcard), and obviously never invite an escort to your own house even if you know your wife will be away (search for those who offer "incalls" at their own premises, or hotels they have booked). Evenings and weekends are likely to be problematic for you, but you can use annual leave to book escorts at times when you're supposed to be at work, or after work on a weekday when you're "working late".