You are thinking of SR4 - where this was a bit more complex but much more sanely handled.
In SR5 there is no separate signal rating, only device rating and the ASDF attributes.
Probably, I've played a lot more 4th then 5th edition.
As to losing the wireles, again I'm not sure if it can be done, but depending on where you have your commlink and how you have to wear the bracelet (and if it even is a bracelet and not some implanted chip or something), maybe you can run a cable from the device to your commlink and then use your commlink to connect to Docwagon. It can lose all the wireless it has if you can wire it up somewhere.
I guess it all comes down to how your GM sees these issues, but I'm sure there are ways to make sure the Docwagon thing stays on, otherwise what's the point in getting it. Of course, if you're out in the boonies, it might be different (and more difficult), but that's probably also in the fine print of the Docwagon contract anyway.