I am about 99% positive that the only time a position player gets injured in the field is the catcher in a home plate collision. So, to answer the original question more precisely, playing ANY player only as a DH does not reduce the injury likelihood at all, other than the very small reduction achieved for not playing a player at catcher (not an issue for the example cited).

Of course, there is always the chance to be injured in a brawl, during which any player on the active roster is subject to injury.