The vice will work but there is a much simpler method:
http://www.remington.com/accessories...unsmithing.htm
Remington Universal Bolt Disassembly Tool
Adding to the company's industry leading line of shooting accessories, Remington has recently released a new universal version of its Bolt Disassembly Tool for use with all Model 700™ rifles including those models equipped with the new Integrated Security System (ISS). Through a simple, three step process, the easy to use tool aids in the safe removal of the firing pin assembly from the bolt of Model 700 to allow for thorough inspection and cleaning. Featuring the traditional "Remington Green" color, the synthetic construction of the tool will not scratch bolt bluing. Small and compact, it is also easily portable.
The information
skeeter 7MM gave you is right on track - the only thing I might do different is I use a wire tooth brush device available in the sporting good section with cleaning equipment - I prefer the brass/bronze brush over the steel but either will work. You must stop rust on the bolt spring so clean it and give a good coat of oil. Be careful what type of oil you use because you need the bolt to work in really cold temps...
If you are using 209's for the ignition and still using the Remington system - I would suggest you look into the Canadian conversion available at Cabelas
http://www.cabelas.com/cabelas/en/te...results1.jhtml
This system provides much less blowback and much easier to de-cap - get the spent 209 out of the nipple..
I have two of the SS 700's and would not trade them for the fanciest new thing out there...