WI: William the Conqueror Can't Bribe Sweyn?

In 1069, Sweyn II supported Edgar Ætheling in his claim for the English throne. A Danish army captured York, but the Normans bribed the Danish to abandon Edgar.

WI Sweyn, for whatever reason, refuses the bribe and the Danish army defeats the Normans in a battle around York in the same year?
How will England be affected? Could there possibly be an independent Northumbria? Or will Edgar be determined to take the whole cake?
Is it possible for the Normans to be pushed out of England at this point?
 
As he had a reputation for not being very successful in battle, perhaps he was playing to his own strengths in discerning his weak hand and doing the right thing -- taking the bribe.
 
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