What's Better: Shaving With Cream On Shabbos Or Having A Goy Shave With A Razor

There is a question that came up in a foreign army [thank G-d that with all of the religious problems that some of our holy soldiers experience in the Israeli army this one has not presented itself] and spawned quite a significant literary output by our poskim: A soldier was forced to shave on Shabbos. If he did it himself then he could use a cream [which is not considered to be a prohibition of לא תשחית פאת זקנך - Don't destroy your beard, but should not be done on Shabbos] if he refused to do it himself a goy would do it for him with a razor [ it's a big no-no to allow your beard to be cut with a razor]. Since we always try to minimize issurim - which one is better?

Here is a treatment of the topic with many sources for those who want to further pursue this topic. It discusses the nature of the איסור גילוח and איסור גוזז and the famous Maharik on מלאכה שאינה צריכה לגופה.

SOOOO EXCITTTIINNNGGGG!!!!