Is there such a thing as peripheral varicose aneurysm, and if there is, what would be the symptoms other than seeing it stick out of the leg?

There are: Peripheral venous aneurysms. Venous aneurysms as a whole are rare. But besides noticing a mass, then often present with pain. Particularly in the lower extremities they are a risk for DVTs or blood clots.

Venous aneurysms: An aneurysm is a localized swelling of a blood vessel usually twice the size of the normal vessel. They are more common in arteries but do occur in veins. Most venous aneurysms occur from the knee down. Symptoms include swelling, pressure and pain. Venous aneurysms are prone to clot because of the swirling of blood within it. Treatments include laser, sclerotherapy and removal. See a vein doc.