Maybe you are allowed to do something like advanced nitrox or tec40 with a single tank and a stage, but then it is for sure no tech and I don't teach it that way. I explain people why this will not work. Single tank and a stage is in my eyes 'Bonaire tech', it works when you want to dive longer and don't have the option to get a twinset. But it is not a good idea if you want to become a techdiver.
The hydros is a recreational bcd. If you had the idea of moving into tech, the shop did advice you terribly wrong if they adviced you this bcd. A shop did the same wrong thing with me and 10 months later I could sell everything again and buy new gear.
But if you want to move into tech diving I would advice you or to rent and dive doubles (but then it takes some time to get used to doubles, so if the course is still only 2-3 days, I would have questions again with the instructor), or buy a bp+wing for doubles yourself and start using that and then do a course. Or go sidemount and get used to sidemount before doing an adv. nitrox course.
In all cases 'starting in a couple of days' sounds not the best idea. Then I would reschedule the course and do it in 'a couple of weeks' to get used to new equipment. And if you are not diving very often in 'a couple of months'.
If you decide to do the course with rental equipment, then you need some dives to get used to the doubles too. But then, what are you going to do after the course? Because if you don't dive doubles anymore, you are not a the right level to move on if you want to do that a couple of months later. Then you need again some dives to get used to new equipment.
Remember, there is no cheap technical diving and only holiday technical diving is not a good idea. If you want to become a real technical diver you have to dive the equipment also on shallow dives in stupid houselakes. You have to practise skills outside of a course. This means you don't need to do all time deep diving, but you need to practise the skills quite often and own your own equipment.