I'm actually a big fan of beta male heroes but I don't see any reason that this guy would necessarily be a beta. Simply turning down this one woman who he doesn't trust doesn't seem like enough to put him in that category. If he was well-liked and respected in town and had a "manly" job you could still sell him as an Alpha.
That said maybe there are fewer publishers looking for beta or regular guy heroes but there are some. I think you should write the story you want to tell.