OK, Teaser, since you admit to being an emmett, I thought we should check Donald Rawe's book on the subject:

Many strangers to the town are mystified by the Mayers' cry 'Oss-Oss!' and the thunderous response from Padstonians of 'Wee Oss!' This 'war cry' seems to be a relic of Morris rather than of Padstow itself. Baring Gould quotes the dramatist John Fletcher (1579-1625) who in his play 'Women Pleased' wrote this speech for a Puritan character:
This beast of Babylon (the Hobby-horse) I'll ne'er back again,
His pace is sure prophane, and his lewd Wi-hees!'
The similarity between 'Wi-hees' and Wee Oss suggests that these are in fact two versions of the same cry.
Violet Alford (Folklore, 1939) interpreted it as meaning 'Come to us, Oss'.
Baring Gould (1889) reports 'Wee Oss! Follow my Hoss!' uttered in a peculiar tone.
Miss BC Spooner held 'Wee Oss' to be an equine imitatory whinny to encourage the Oss, and quoted an old Padstow woman as saying, 'He's pretty wheeing'.
But, comparing Fletcher's speech with Padstow practice, it seems certain that it was originally a cry to encourage the Oss to capture and mate symbolically with the woman he was pursuing.
Thurstan Peter says that 'O Wee Oss' was shouted in 1913 by everyone when the Oss pursued some 'victim'.
Miss Alford, in 1968 recorded that Swiss carnival hobbies recited poems and ended them with 'Whee-hee' and declares that traditionally, and as recorded by 'our Elizabethan dramatists' this should be answered by the female 'Ti-hee'.
The derivatation of 'Wee Oss' therefore appears to be from the horse-whinny.

So there, take your pick!
Oss Oss,
Wee Oss!
Robyn