I have been in the Austin swing scene for a while and can tell you it is a TRUE hott sexy blast, WHEN DONE RIGHT!! There are a few clubs in Austin that might work, however, the trendiest one currently is Players of Austin located in North Austin. I would avoid all the other swinging clubs currently, as they have all changed owners recently and have not been kept up. A few of the newer websites that locals use are:
www.kasidie.com
www.sdc.com
With all this in mind, I would still have to agree with a few of the comments above, I would most deft go pro or find someone that you have no personal connection to. This being a "first" for you two together might also open a can of worms/ emotions that you might no be ready to deal with after. Therefore, by going with someone who has done this before or with someone that you do not have a personal tie to, will help in avoiding any weirdness after the experience. I have ran into many couples that have had their first 3some with friends, only to find that it has ruined their friendship after. Find a provider that you are truly comfortable with, and arrange a time that you and your wife will be out and about, where the provider breaks the ice by approaching your wife first ... Hopefully after a few cocktails and some flirting, she will break out of her shyness!
Good Luck!