Dog Chewed USB Cord on Wheel help :(

So my 6 month old lab got left alone in room with wheel and chewed usb cord in half. I have considered just soldering it back together but wanted to see if anyone has any experience doing so with a usb device and could warn me of any possible pitfalls. My current plan is to solder it and then shrink wrap each individual wire and then tape the 4 of them down to main wire to keep them from getting caught on anything. My only concern is cross talk on lines causing issues since there is shielding and a twist inside on the usb cable and will not be any in between cables or twist with my intended method of repair. Any one have any thoughts on this or experience?

Two things:

1.  Think of this as an opportunity to upgrade you wheel, and

2.  FORGET the notion that you will actually get your lab to stop chewing stuff.  Labs chew to relieve stress.  The key is to give him something that you want him to chew and make sure it gets shoved in his mouth every time you catch him with some other thing that you don't want him to chew.  Our 3/4 black lab-border collie cross  (Apollo) is given the largest pressed raw hide bones we can buy - not regular raw hide, which is too soft - pressed raw-hide.  Also, regulate his time with them as injestion of too much at one sitting will give him the runs.  However, regular chewing will also keep his teeth clean, so that's good too.  Here's a picture of him at 6 months old getting busted for stealing a toy that's not his!

Attached is one of both of us.  If you wanna canoe with your dog you better have a real good command of him!

Oh, did I mention: buy another wheel?

 Yea it was totally my fault he chewed it, I had him confined to upstairs with no chew toys and left him alone for about 10 mins. I have pretty much gotten him now where he only chews on his toys unless I leave him without one and he gets bored. So I call this another lesson learned. Really cant do a new wheel at this time so I'm hoping I can fix. Here is a picture of the guilty one

I don't think interference will be a problem for the reconnection solder like that.  Another option, especially if you have spare usb cable laying around (who doesn't), is to attach a new cable internally.  That probably is a soldering job too, but won't have the snagging-on-stuff worries later.