I agree with roverhi. You don't need a high tech jib
halyard. All you will do is spend money
for no perceivable advantage. Go with whatever low stretch poly is cheap
at your local chandler. Samson
XLS would do fine as would NE Sta Set X.
Cut the splice off your old halyard and get a rigger to splice the snap shackle onto the new one. Sew the tail of the new halyard to the cut in the old one with sailmaker's twine and use the old one to pull the new one through the mast
. You will have to burn and whip the cut in the old halyard just a little so that the join doesn't fall apart when you are half done.
3/8" poly would do the job and if you want Dyneema
you would only need 5/16". That will create a new problem in that the 5/16" will probably cause your clutch
to slip. Most cannot handle less than 3/8". In order to help the clutch you will have to pay extra for 3/8" Dyneeema which, in terms of strength, is totally OTT and would suit a 40 footer.