Woosie's 64 was his lowest round in almost 18 months and helped him leap to the top of the leaderboard at the halfway stage.
But 20-year-old Dougherty, who has already finished second on the European Tour in this his maiden season, hoisted himself into position to go for his first victory as he shares second place with Warren Bennett and Australian Stephen Leaney.
He eagled both of the par fives on the back nine to come home in 32.
He said: "I got off to a good start with birdies on the sixth, seventh and eighth, which are not easy birdie holes.
"The two eagles on nine were a bonus."
Mark Pilkington added a three -under-par 69 to his opening 65 to lie just two shots off the pace as he chases his maiden European Tour triumph, but Macclesfield's Jamie Donaldson, one off the first-round pace, slipped to a 71.
There was also good news for many of the Ryder Cup players in the field, with Padraig Harrington leading the way on nine-under-par 135 after a six-under-par 66.
The Irishman has struggled with various injuries over the past few weeks and strained the right side of his neck on the range last night but shrugged off any discomfort to record eight birdies with just the two dropped shots.
Playing partner Colin Montgomerie also carded what he described as a very comfortable 66 to move to seven under par, alongside Thomas Björn who shot a 70 and Lee Westwood, whose 67 represented his best round of the year and a strong indication his form is returning just in time to face the Americans at The Belfry at the end of this month.
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