A small pencil torch and a Sta-Brite silver solder kit will make very short work of the soldering. I found the torch at my local hardware store for $3 and it's refillable with canned butane used for lighters. You just clean the parts with scotch-brite/steel wool, put a drop of liquid flux on the parts, assemble the parts and secure in position, touch the flame to the joint area untill it's hot enough to melt the solder. When the solder melts, it will flow into the joint all the way through. Let it cool and wash the flux off. You can then use the scotch-brite/steel wool to polish up the joint. I'll see if I can get a pic of my torch posted shortly.

OK - Here's the torch.