The Alaskan should be a 1958. That was the first year the Alaskans were sold and the last year before Bear put the coins in.
If you can give a description (or pic) of the Polar I can date that one for you. I collect the 50's Polars.
The brace on both boths should be in the 7" range plus or minus a little. They were both made pre AMO and the length of the bows, even within the same model and year, can vary by almost an inch even though they were all marked 62" or 64". Gets to be a pain when ordering strings or switching them between bows! Your best bet would be to measure the string that's on the Polar and find a temporary string to brace the Alaskan and measure it. Measure the string length under tension.