Hello Kieran,
First of all – this winter was so mild the chances are that your colony would not have been broodless in January and that’s probably why the oxalic didn’t work.
I’d worry about shookswarming a 3 year old queen unless she was still good and strong – it’s a pretty stressful thing to do and it’s still quite cold. Have you got drones?
If it’s just varroa you are worried about – you could try again with Apiguard when the temperature comes up a bit (15 degrees).
However, the honey flow is approaching (hopefully) and you won’t want thymol in your honey.
You could consider MAQs as you don’t have to remove supers, the formic acid won’t get into your honey (if there is any) and they work at 10 degrees or above – brood or no brood. But that can be hard on the queen as well – it can cause a failing queen to be superceded. Not always a bad thing.
Once you have drones, you could consider taking away your old queen in a nuc with lots of bees and just a little brood, leaving most of the varroa behind. Meanwhile, the original colony will rear a new queen for you. During the short period they are broodless and before the new queen gets laying, you could trickle (or vaporise) with oxalic acid.
If that manoeuvre was to work, it would fend off the varroa for the season and get you a new queen as well.
If the original colony failed to get a new queen laying you would still have the old girl in the nuc.
Hope this is helpful.