Do whatever is comfortable for you. I have never heard anybody ever comment negatively on such a thing. You will be different that the majority, but who cares. Most players don't use two shoulder straps because we use the thumb strap. If you don't strap your thumb in (like the triple row players) then you need two straps or the accordion will not be anchored. The thumb is what anchors the right side of the accordion and is what keeps the left side bellow movement from moving the keyboard side. If you feel more secure with two, then use it, but you shouldn't really NEED ANY straps if you right thumb is used in the "Cajun" method properly. But you need to do what works for you...everybody's body/shoulders are different.
For those of you that are having trouble with the strap slipping off of your shoulder, I recommend having a strap made with the suade side on the "inside" (against your shoulder.
I had Danny Dyson make me one and it is great!
It "sticks to your shoulder and no more sliding straps!
I really appreciate everyones feedback and encouragement. I have found that if I split my 3/4" strap down the middle, I can play either single or double strap. But, I prefer double strap. I can double strap and walk around and play all day--now my wife and dog can't hide from me. Also, I want to let Chris Miller know that I finally transcribed and learned Frisco Zydeco--a conjunto sound. Now if I can just get it up to speed. Thanks Chris.
I play all my cajun and tex-mex and Chris's Frisco Zydeco on my single row. I only play a single row. Chris was very encouraging and yes it can be done. My Martin is wet tuned 5 cents and I close #1 and #2 reed banks. You get a pretty authenic sound. If you dig a little you will find that the single row was used for conjunto in the beginning but soon switched to the double row. You can still find a few old timers like Wally Gonzales who play some conjunto on a single row. He also plays a mean toy accordion.
Two straps may not look "cajun" but if its any comfort the accordion is not "cajun". We "adopted" it back a few years ago. Like everyone says, nobody cares what it LOOKS like, its the sound that gives us the warm fuzzies.
I play with two straps(one over each shoulder) and center my thumb behind the keyboard. Been playing like this since 85 and I'm passing a good time.