offer for vs. offer to
Both are OK, although "of" would be better than "for" in example 1.
The confusion arises because the word "help" can be either a noun or a verb.
In the first, "help" is a noun. A close paraphrase would be:
He refused the organisation's offer for assistance.
But the following sounds better and more natural:
He refused the organisation's offer of assistance/help.
In the second, "help" is a verb. A close paraphrase would be:
He refused the organisation's offer to assist.