Case
I filled my case with polyurethance foam - this is often called upholstery or cushion foam and can be found in a hardware stores.
It would be very convenient if you could cut polyurethane foam with a hot wire cutter or an electric craft pen cutter as you can with styrofoam.
Many people do this and it clearly doesn't kill them but it seems it's not a good idea. It turns out the crucial difference between styrofoam and polyurethane foam is that styrofoam is a thermoplastic while polyurethane foam is a [thermosetting polymer]. What this means is that heat will cause styrofoam to melt while the irreversible curing that occurs with thermosetting polymers means that while a hot wire cutter or electric craft pen can cut through such material they are doing so by burning rather than melting. And the burning releases very unpleasant chemicals. How unpleasant seems a matter of debate - manufacturers downplay the issue (e.g. this document from Dyplast Products) and some companies offer hot wire cutting of foam as a service, e.g. see this page from Foamcraft which includes a video showing them cutting foam this way and while a fume extractor clearly is used, they're clearly not treating the obvious smokey fumes as very toxic.
Many companies also offer laser cutting of foam for tool boxes etc. There's a nice instructable on doing this yourself here (with polyethylene (PE) or ethylene-vinyl acetate (EVA) foam rather than polyurethane). Obviously laser cutting works by burning - so clearly one can do this, the question is how good a fume extractor do you need. One should never cut e.g. PVC with a laser cutter (as this releases dioxins) but there's no clear advise out there for polyurethane. Some people claim the fumes are little worse than those given off by burning wood (though people underestimate the fumes invovled there) and others claim more deadly characteristics.
So it's hard to categorize the risk - it clearly isn't immediately deadly but if you read about the compounds released as a result of burning polyurethane foam then it sounds potentially deadly. But then so does e.g. taking aspirin or any other common drug if you just look at risks section of the accompanying leaflet.
It seems you should cut the foam with a scissors or a knife. I tried both and got the best result with a craft knife with snap off blades (this this one) - I fully extended the blade to get the maximum blade length and used it like a saw to cut through the foam. While it's easy to cut along lines and curves that you've marked out on the foam it's very hard to make corrections later as it's very hard to just shave off a few millimeters of foam from an existing edge. If anyone has any tips of tricks on how to do this I'd be interested to know.
Sharpness seems hard to gauge with these blades - I found that a cheap no-name craft knife cut much better than a more substantial and expensive one I bought.
While I didn't try it another common way to cut polyurethane foam is with a standard electric kitchen knife (like this one). There are lots of videos on YouTube showing how to do this, such as this one that contrasts cutting with an expensive professional foam cutting tool and with a kitchen knife. It's easy to hold a craft knife and cut fairly precise curves, an electic kitchen knife looks a bit more ungainly so I don't know how it would work out for curves, but it might be better at biting in along an edge to shave off more foam - something that's very hard with a knife.