First of all, let me commend your courageousness. If you have surfed through many of the forums and threads contained herein at Audioholics, you will know how the vast majority of members feel about Booze products. Myself included. My gripe is mostly with their speakers and the prices they charge and not provide a quailty product comensurate with that price, spring loaded speaker clips are just a starting point.
Be that as it may, to answer your question, yes indeed, the aux outs on the flotsam you speak of are RCA jacks. Your problem, though is not just connecting this cable to the speakers you have. The aux out is a line level signal, not a speaker level output. This output is designed to go into a tape deck or amplifier or self powered speaker. The 151s you have are not self powered (no amplifier), therefore you will need a seperate amp.
You can find a PA style amp cheap, or monitor amp on ebay or ZZounds, Same Day Music, etc.. Probably about $150 - $200. You can also find powered outdoor speakers for about the same price or less.
If you still want to do this, I recommend the buying the amp, (will also recommend the Alesis RA150- 45 watts/channel, Class AB, high signal ratio, low THD, etc.., and about $150 after a thorough search) it will have more and better future uses as you upgrade (as you most likely will) from Barf - I mean booze- er bose. For outdoor speakers, you do not need an audiophile type amp such as those you read about here, a PA or studio monitor style (the Alesis is a studio monitor amp) amp will work just fine.
If you want to real cheap get a three piece set of computer speakers and use the subs output to drive your 151s.