FATE seems to know the layout of your bedroom
It would be rare to find a couples bedroom without a chest of drawers in it.
A cot is about the same size as a chest of drawers. So if a cot fits in the nursery, a chest of drawers probably would too. If a chest of drawers fits in your bedroom, a cot would too.
Hell, I would even remove the wardrobe along with the drawers if I was so desperate for space. Definitely the cot needs to fit in the bedroom, ideally next to the bed.
The process of getting dressed in a morning changes in a way that non-parents don't realise. DH getting ready for work, for example - you'll end up getting annoyed with him making noise as he opens drawers and fishes around in the wardrobe for a shirt while baby is asleep. Certainly no lights on to disturb baby. So moving drawers (and wardrobe) into another room while baby is tiny is not a bad idea even if you have the space for a cot.