I was looking for a similar thing recently and have even less space (no shed) so it had to be small.
After much deliberation, I went with the Makita DVC750 cordless dry/wet vacuum. It gets some good reviews (apart from average suction) and i had Makita batteries already. Had it a couple of weeks now and I wouldn’t say Im amazed (yet). Its way louder than I expected and the suction is ok (but maybe it doesn’t need to be that great for saw dust). Fits on my Mac allister track saw and katsu router fine and functionality it is very neat and works well. Also very solid.
The similar Milwaulkee gets good reviews, so might be worth seeing if there’s a battery adapter available for your Dewalt batteries.
Alternatively, there’s a very small corded vac in Lidl at the mo for 30 quid. Get that and one of those e-on power down plugs for Power take off.