I'm not a fan of using a tether either but your circumstances and situation are a bit unique. They water you sail in is usually very cold and the amount of time that a rescue would require could become an issue. This makes staying with the boat a little more of a priority and the risk associated with a tether somewhat more acceptable, IMHO. I would first examine the type of connection you are using for your tether...I presume, given that it clipped you and itself to the shroud by accident that it is a carabiner type?
I would use some type of snap shackle on the end of the tether that is not likely to clip itself to something without a very distinct interaction on your part. These also have the benefit of being able to release while under a good bit of load too - meaning that if you were being dragged underwater by it, you would have a chance to release it if necessary. Be sure to install a significant release line to the release if you use a shackle like this (I would knit a small line into a wider, very grippy, short tail and attach it to the release pin).
Also, upon further consideration, I might also be inclined to try a surfboard style ankle tether that attaches to your ankle with several overlapping layers of velcro instead of attaching to my harness - perhaps coupled with a snap shackle connection. My thought is that the ankle tether would be less likely to become obscenely tangled than something connected to your harness. It still wouldn't be great if you are being dragged behind the boat, though.