Hi John, no you don't need a new spring, but the recoil starter is overdue for servicing. This is a fairly easy operation and does not involve replacing any parts, but it does need to be done carefully and line with the Briggs and Stratton instructions. (I take it your SB45 has a Briggs engine, as most of them do. If not, please say so. Also, if you give us the long series of numbers stamped on the sheet metal cooling air cowl of the engine, we can tell you its date of manufacture, among other things.)
The page in the B&S overhaul manual dealing with servicing the rewind starter is here:
http://www.tpub.com/content/recoveryvehicles/TM-5-4240-501-14P/css/TM-5-4240-501-14P_163.htm(Note you can go forward and backward from that page using the "back" and "next" commands at the top of the page: the whole overhaul manual can be accessed in that way.)
Essentially, you just need to clean up the parts and put one drop (plus or minus zero, or you will cause yourself problems) of good-quality engine oil on the end of the crankshaft extension. The original equipment single drop of oil has finally been used up, after 25 years, and needs replacing; hence the squeal. While you are in there, clean up the parts, especially the balls and ball cavity, but do not lubricate them in any way. Any kind of lube in the ball cavity becomes sticky eventually, causing the sprag clutch to stop working.
You will probably find the B&S instructions self-explanatory, but if you have questions, just come back here and we'll try to sort them out. I'll leave this thread open.