A bit late now, but your tup will have been appreciating the female hormones floating around the farm (don't have to be sheep hormones, anyone will do including human. Don't have to be female either, it's just a randy time of year) for many weeks now, with accompanying testosterone, so a little trip in a trailer won't make much difference!
The way to minimise tup taint in meat is to avoid sending them for slaughter at this time of year. You don't say what breed you have and I only know about Primitives which we have always sent off at 16 months, that is August for Hogget.
Of more concern is the ewe who will almost certainly be well mated by the time you arrive at the slaughterhouse. She will then be penned with the males so that will continue until they are taken in. Whether that's distressing for her or not is your decision to make.
We always speak to the slaughterhouse in advance hoping to get them taken early, but it does depend on the size of the facility and how many commercials are going through on the day as they don't have time to mess about.
If it's any comfort, we still have an hermaphrodite ewe who we've been trying to send off for years, but for the same reason she's still here, thinking she's a male and bossing the ewes around