I expect it takes the standard singer needle - they have a picture of it right on the front slide plate - actual size too.
Older Davis machines take a much longer needle, so I guess Davis wanted to take extra care to make sure people didn't use that one in the newer machines.
I have the manual for your machine, if you would like a copy, may take me a while to get it scanned though.
I may have a few extra shuttles too, not much time to dig right now.