This is not an easy one as it sounds like you shouldn't use oil-based poly in your workshop as you might normally as it will transfer the smell to the rest of the house. Never mind the health concerns (at that low concentration it's not likely there'll be an issue) but many people find the smell unpleasant, some even nauseating, so on that front alone it's worth going a different route.
With oil-based finishes usually you can successfully reduce the released solvent vapours by using 'odorless' mineral spirits which although not truly without any odour can be damn close1 but the smell from the regular spirits used in the polyurethane itself might be enough alone to make you not want to use it.
Alternative 1, finish in a different room
I started woodworking in my kitchen, and as you can imagine when it came time to use finish I wasn't very popular if I was using regular poly, so I very quickly changed to finishing in a spare bedroom. With the door closed and one or more windows open the smell just outside was barely noticeable and I got reasonably good drying (although not as good as if I'd been able to leave the door wide open to maximise airflow).
If you don't have a spare room that you can use for finishing for the next week or so I think you might need to look into using a different finish.
Alternative 2, go with waterbased
The best of the waterbased finishes are now really very good in terms of the level of protection they provide — equalling that of oil-based polys, at least in short-term testing — and while they typically don't make the wood look as good (there are workarounds for this if needed2) they are very low-VOC so both very safe to use indoors (even in an enclosed space) and what little smell there is is not at all objectionable.
Waterbased finishes typically quickly and reliably so as long as the temperature is not too low, which sounds like it wouldn't be a problem in your workshop.
Here's what I might do
One of my favourite finishing strategies would minimise strong solvent odours and it falls firmly in the looks-great-doesn't-take-long category. It's a three-layer process, which sounds like it would be slow but it's not, it's both very fast3 and very important to me, makes almost all species look excellent.
You start with BLO, then build the finish with shellac, then topcoat with poly. I would prefer to use oil-based poly for this, but you can substitute waterbased poly if you feel you must, the wood will already be looking excellent from the preceding steps.
I first learned of this some years ago online and then couldn't remember where I'd read it. I don't know if this was my original source (many things get 'shared' around online without attribution) but I found it again during the year here on the Woodsmith site, A Fast & Durable Finish Recipe. Note it can be downloaded as a PDF to your hard drive for easier reference.
1 Most people can't really smell it at about arm's length.
2 For example pre-treating the wood with BLO.
3 Takes a day, two at most.