All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
What we can do, is underline the permissibility of cutting the heads of these statues. Abu Hurayrah reported that the Messenger of Allah, sallallaahu ʻalayhi wa sallam, said, “Jibreel (Gabriel) came to me and said, ‘I came to you last night, and nothing prevented me from entering except that there were images at the door, and there was a curtain inside the house with images on it, and there was a dog in the house. So order to cut the head of the image in the house so that it becomes like a tree stump...’” [Abu Dawood]
As for the manner of doing that, it is up to you to decide. You will surely find a way to cut the heads, given that we live in an age of modern tools that cut steel, let alone plastic.
You asked, “...and even if I successfully removed them, the issue then is what I do with the toys' heads?” The answer is that you can throw them in the trash or any other disposal site; it is a simple and easy task, by the permission of Allah.
Allah knows best.