From Southport (not Cheshire I know) I always go to Preston then A59 to just outside Harrogate, then Ripon bypass, little white rd s/post Sharrow this takes you straight to the A19 then A172 to Guisborough, then A171 to Whitby. I have gone this way since sitting for an hour on the York bypass. On paper it's surprisingly, slightly shorter than M62 York, Pickering, but takes about 20 mins longer, but so less stressfull.
Cheers
Les