Can I choose the spearman as claim for a mil challenge then while he is moribund response to put him back into shadows thus saving him from being killed and use his effect?

No - a card, once its moribund destination is set, can not have its moribund destination changed except by a replacement effect (that uses the word "instead", or is Call of the Three-Eyed Crow). The FAQ further specifies that you can't use it to pay costs of discarding/killing it, which, as this is written "put him into shadows TO choose a character", is a cost.