"Correct bayonet" is subjective
I collect some US militaria and there's a big push in some circles to have "numbers matching" or "same year" stuff. That's all well and good if you also understand that for instance, with your 03A3 there was no rule that said "the following bayonets are to be issued to Model of 1903A3 rifles only"
An M1 bayonet, an M1905E1, or a Model of 1905 are all correct in my opinion. if you're looking for a WWII issue bayonet, then obviously anything 1945 or earlier would be the thing
You may wish to have anything '43 or earlier but I can also say with surety that in 1944, if a GI with your 03A3 needed another bayo, they wouldn't hunt up a '43 or earlier example for him
Nickel played oilers used to be around, the Collector Source was a great place:
http://www.thecollectorsource.com/page/1219295
But I note that they are now out of many items and do not expect more. I should have bough an 03A3 C stock and some nickle oilers when I had the chance and now I regret it
Try gunbroker (you need to know what you're looking at and for of course) and try
http://www.usmilitariaforum.com/forums/index.php?act=idx
Of course, to buy and sell you need to be a member, and they aren't really a clearing house or store- they are enthusiasts, like you and I
bear in mind that neatsfoot oil can (not must) damage the thread in the sling
Does the sling have brass hardware or steel?