Wait wait wait... wooder as in wood-er, with the same oo as in book and cool?
What kind of proper English!


(to me as a European, proper English is British English ;-) )
I would use the the same a in water as how the British would say the au in laugh.
if I pronounce the t as a t or a d probably depends on how fast I speak and whether or not I speak with a Brit or not.