Does anyone know what gauge wire is used on the receiver?

looks about 24 AWG but don't quote me. The length is the more critical factor.

Any grade will do.

You can buy a new one from Tower for about $3.50

You can buy 35 feet of it at RadioShack for less. I replaced one with 24 gauge stranded wire. The wire is the same and the protective coating is just a little thicker. If possible, dont get into the RX box but splice it with the antenna already sticking out. That will help isolate the heat from the electronics when you solder it.

Soldering in the middle of the wire is a very bad idea, it's too easy for the joint to break because it's succeptable to vibration. If you're just a little carefull with a soldering iron you can replace an antenna in just a minute or two. There is no risk to the electronics inside so long as you don't intentionally hold the soldering iron on the board for more than about 5 seconds. Use a dot of heat shrink tubeing at the base of the joint to strengthen it and you're all set.

I've not had it break but I do use heat shrink on it and dont place it in tension. I replaced it between the RX and the stress reliever before the antenna tube. Your right in that soldering to the RX is no big deal but some people seem to build their helis with sledge hammers.