It is highly unlikely there will be any audible difference. The audio quality of an mp3 file is decided by it's bit rate and how good the encoder is.
In almost all cases you want to do as few re-samplings as possible, as it is a bit like making a copy in the analog world. In the case of mp3s, if you have a 96Khz source it has to be re-sampled to either 44.1 or 48Khz, as mp3 doesn't support 96kHz. A good decoder will probably not have to re-sample the bit rate before encoding, but that extra information will instead be thrown away during the encoding to make the data fit in the mp3 bit rate.
If there is an audible difference it's in that case because the decoder you use are bad at changing the sampling frequency from 96kHz to 44.1. In that case you might want to change the mp3 file to use 48kHz instead. But with modern encoders I find that unlikely as well. But should this be the case, re-sampling it to 44.1 or 48kHz in a program that does such re-samplings well could be an option. Re-sampling to 16bit from 24 shouldn't make a difference assuming your sources peak volume is reasonably close to max.
Should the peak level be extremely low, you may lose information that the mp3 encoding otherwise might have kept if you used the 24 bit source. But for that to happen I expect you would have to have a peak volume that is around 8 bits lower than max, which means that you could raise the volume 256 times (or 48db), which seems unlikely.
In the end though, all you can do is test both, and have a friend make a double blind test with you. :-) But if that doesn't work, just use the original source without re-encoding it first. It's likely to give the best results.