Hello Michael
Good luck in getting an appropriate 2 3/4hp Douglas - they are around. As to riding them, they aren't difficult at all. The 2 3/4 is a physically small and light machine, and the twin cylinder engine is so easy to start that you can paddle them with your feet - no need to run and jump like on many veterans. The levers are not complicated, and you don't need to fiddle with them constantly. And of course they aren't fast, so they don't feel like they are getting away on you! This isn't the case with my dad's 1924 OB 600 ohv, which is very fast, and in all honesty is a bit daunting to ride in a built up area. Great on the open road though.
If you are an experienced rider on any type of motorcycle, I think you will have no trouble riding a veteran Douglas - they are leaps and bounds ahead of most machines of the era - which is why they were so popular.
Might I also suggest that you that you get in touch with the local Vintage Motorcycle Club, as well as the Antique Motorcycle Club -they are also Victorian based. I'm sure that someone will let you have a ride on a veteran if you show interest, and might even know of a suitable Douglas for you. Check the archives on this list too - there have been a couple of veteran 2 3/4 machines for sale.
Cheers, Graeme