I would be worried that the squirrel would hurt Morphy. This is the dog whose response to coming face to face with a badger a few weeks ago was to wag in a friendly fashion.
Many moons ago, when my dad kept hens, we had a rat problem. The hen houses, which measured 48' by 24' and each house 100 hens, had sliding doors that were often difficult to close tightly because of chicken dung and straw debris getting in the way. Where a gap of about half an inch existed, the rats widened it and obtained access to the hens' food. We would operate a pincer movement, my brother and I. Late at night, when the hens were roosting on their perches, we'd block the rats' exit with a rolled up newspaper, go in the door at the other end of the house, corner them whilst dazzling them with bright torches and I would then wade in with the cricket bat.
Only once did we make the mistake of sending the dog in after them. The black bit of his nose was virtually bisected by a rat.