The 1907 LDS vest-pocket edition replaced the conditional modal would with the future modal will. It is possible that would sounded too conditional here. The 1911 LDS edition followed the secondary reading, the one with will, perhaps by reference to the 1907 edition since the same change of would to will was made in both the 1907 and 1911 editions in 3 Nephi 3:15 (see the discussion under that passage).
This change away from the conditional is, of course, not really necessary. Such usage involving conditional modals in expressions of the form “I pray that S”, where S is a clause, occurs elsewhere in the text—and without variation:
The critical text will restore the original would here in Moroni 9:22.
Summary: Restore in Moroni 9:22 the original conditional modal would in “I pray unto God that he would spare thy life”.