I say Yorks-hur... I dunno why!
I live in Nottinghamshire in the UK and the "shire" is pronounced "Shyer"... I guess that Yorkshire would be pronounced the same with the "Shyer". The accent of people from Yorkshire is very drawn out and people I know from there pronounce Yorkshire like "Yorks-hi-errrr"
I personally tend to say "Yorkie" though... I like to take the easy route... same as I like in "Notts" not "Nottinghamshire" LOL