You will notice that as a general rule steel stacks commence to weaken at the first half-dozen sections from the top downward, or at the band. The rain hitting the in- and outside from the top, and lying around the band, is causing the rust to form more quickly than on any other part of the stack. This accounts for the aforesaid parts weakening the quickest.
It is always wise to sound a stack at the top and band so as to determine whether it will stand much tugging or bouncing upon. If it looks weak and you make up your mind that you will go through with what you are doing, I would suggest that you do all the pulling and take just what tools you can possibly get along with.