My suspicion would be that it's not of intrinsic historic significance by the definition that only exemplary objects would be considered to be so; but that it is of significance because it's a rare survivor of something once commonly found.
I very much doubt that replacing the timbers would be much of a crime, particularly if it were to ensure the crane's survival. Furthermore, I don't think that replacement of the timbers would be a particular detriment to its historic significance - anything like this containing a lot of timber is likely to have had most of it replaced over time, so there's little difference with replacing timbers now compared to doing so when it was in use.
Hello again darkness, my old friend...