Yoli here,
Thought I'd drop in pre-trip-to-office.
Sex without urges? Well, I'd have a hard time recalling any occasion when I had sex without urges. Then again, I still have my little hormone makers...my ovaries, so I may not be "qualified" to opine.
For all that, there have been times when I was not the initiator. As an example I there are occasions when I come dragging in and am thinking only of a warm bath or a soak in the pool. Sometimes Ash(leigh) joins me in the pool or shower, or kneels beside the tub to wash my back or just chat. No matter how tired or bummed I am her touch often triggers further...uhhhh...activity.
Since the original question posted here is more directed toward males, especially castrated (chemically or surgically) males, the only contribution I can make is that based on observation of, and communication and intimacy with, Barry, my eunuch friend/lover. Barry has always been quite forthcoming about his sexual "condition" as the interval since his castration increases. We've discussed this topic on numerous occasions over the few years I've known him.
I also have had occasion to "interrogate" one of his eunuch friends (the one from Houston) to a lesser degree.
Neither Barry nor his friend experience sudden urges such as might be expected of an intact male, at least not in a manner one might consider within the norm. Barry, though, says his desire to be kind to, and please, others, drives his willingness to engage in intimate behavior. I hasten to add that he is NOT promiscuous! There are very few persons in his sexual circle, and Ash(leigh), WOBG (when she's here,) and I comprise half his "crew". The others, of course, are males...including one who is in intact though extremely effeminate. The other two are surgically-created eunuchs. He has no "butch" boyfriends.
One might say that Barry senses the sexual urges of others and willingly engages in sexual activity in order to please and satisfy. Once things get rolling, his own more basic urges kick in, though not with the urgency usually felt by most intact males (or horny girls like me...Blush!)
Since castration, his centers of arousal have become more of an oral or anal nature rather than in his penis. Make no mistake; That sweet little morsel happily welcomes loving attention, but it is not the first place where his arousal originates. Obviously, he never suffers what I've heard termed "blue balls."
According to Barry, as intimate activity progresses he starts to feel an increasing "need" in his penis as well as what he calls an "urgency" in his prostate. This doesn't always
lead to a genuine stiffie, but usually does engender a partial erection that is often sufficient to effect entry into my (or someone else's) little >^..^< or my other Port-of-Entry. Needless to say, no matter how erect his peepee (or not) giving him oral loving care is a snap. Unlike BigGuy's impressive equipage, Barry's never makes me wish I could unhinge my jaws, ala Boa Constrictor. After all, at maximum readiness Barry's is no more than five inches long and very "svelte"; More like sucking on an Oscar Mayer weiner than BigGuy's kiolbasa.
So, do I ever have sex without urges? Well, maybe for the first nanosecond.

And Barry? Well, yes, he does but urges DO set in fairly quickly. He says that, as an example, if he were to drop to his knees and pleasure me or a man and it lasted no more than maybe three minutes before my >^..^< or someone's

"gave it up", then he'd be OK with walking off without further fun and games. Otherwise, he'd soon be wanting a little TLC for himself.
Let's face it; The relationship, irrespective of sex, should be the determining factor. If all else is in balance, sex will sometimes occur. The real test of intimacy is what takes place before and after sex...whether in the bedroom or on the street.
Not the most scholarly little exercise, but it's what I have learned so far.
Hugs and occasional gropes,
Yoli