Yes I trust.
Discretion is the cornerstone of their business.
Well that's the risk you take.
If you want a 100% gaurantee that nobody will find out, the most fool proof way is to not do it.
Every adventure in life carries some kind of risk, and being found out and dealing with the consequences is the risk with regards to this type of adventure.
They are very unlikely to even acknowledge you if they see you on the street, especially if you are clearly there with someone else.
The SW isn't your bestie, they are a person with whom you exchanged money for a discrete service.
There is at least one thread on this forum that tackles this question, and a number of SWs have made posts on that thread, the common thing was maybe exchanging a brief glance or smile at most.
Might happen that you are recognised at the door and turned away because they know you (again in some threads here SWs have mentioned this).
But unless it is your partner's best friend, and your partner knows that person does SW, this is a very unlikely scenario.
For the most part the people in SW's lives do not know that the person does SW, they want to keep it that way.
So if the SW goes up to your partner and tells them that you attempted to make a booking, the first question your partner is likely to ask is "how do you know" which would then be an awkward conversation for the SW.
But again, discretion is at the heart of their business, if you were turned away because you were recognised that would be the end to the situation in 99.99% of cases.
Noticed this duing the short time I lived in Wellington.
Doesn't worry me because I don't live there, and never would again, at least by choice.
But again, discretion.
The booking lasts as long as you are there, then it is over, both you and the SW move on with your lives as strangers.
They don't want to out you, or run up to you on the street and plant a big kiss on you, or anything even remotely like that, as anything like that is more likely to harm their business than anything else.
It is a job to them, not a love affair.