It depends on the region and how fast you're talking. I believe there are similar issues in British English with syllables ending in "r" preceded by the back vowels. In my experience, most Americans say "tord" when speaking at a normal rate.

I prinounce it with the 'w'

Depends where you are some parts of the USA pronounce it as tour and others pronounce it with the 'wha' sound Toured Tou ward