Could cut it off a few feet up first.
Are your squirrels likely to be proper native red squirrels or horrible invasive alien North American tree rats?
I'm afraid I'm going to have to hand dig them as my garden has no access for machinery, more's the pity. I'll just have to take my time and cut them into sections.
Re squirrels, alas they'd just be the grey ones as the only red squirrels round here are isolated on Brownsea Island.
Quite a few birds nest in leyllandi, including blackbirds and the goldcrest.