DD was pretty tiny (5 lbs) I used the bummis preemie ones and they were fine, but if you have a bigger baby, they will be too small. Her umbilical cord lasted for 7 days.The bummis preemie covers would need to use the tiny prefolds as well.
I'd say go with disposables until it falls off... but really, a pack of disposables is $20 anyway...and you'd probably need at least 2-3 packs...so it would probably be just as well to get 2 of the nb covers w/ the cut out. (Thirsties XS has it too... and they fit 6-12lbs based on their rating, 6-10 in reality... they happened to be too big for DD at first, but she was an exception)
I'd do the thirsties xs if I were you...they'd last longer size-wise than the bummis. I'd only get two. You can manage to rinse it in the sink between washes if necessary. Plus you can sell the covers after you are finished, or use them if you have more kids later on.
Thirsties duo wrap is great for the next size up.