We had My son in a basinette for about 7 weeks , we would wrap him in a muslen wrap and put a blanket over the top and tuck it in the sides.

With the cot we did thet same thing , we had just a fitted sheet then wrapped him and put him at the end of the cot then tucket a blanket around him in the bottom and the sides.

As far as SIDS goes i think they just recomend a fitted sheet.