This is the correct answer - I know because I was there 10000 years ago and had to decide between this and buying a special case from koolance. Amusingly they still sell one for the outside.
They can also be handy if you have to do anything weird like route display cables from the GPU to the motherboard like for a thunderbolt display.
I believe you can change the scaling algorithm obs uses? Right click the source and go to “scale filter” is what Google is telling me, not at a computer right now. I think it defaults to bicubic which should be ok though? The switch does its own internal scaling a lot of the time and that can look pretty bad though, but unless you get into some serious shenanigans that’s basically baked in.