I have researched this. well not this specifically; but Latin in school.
This was taken off a site that I use to use for reference. I was never told by any of my professors that I was using incorrect pronunciation.
They even describe how to enunciate the word Pilum specifically.
PRONUNCIATION GUIDE
a = as in "ah"
ae = "eye"
c = always hard like K
g = always hard as in "girl"
i = short as in "pit", or long as in "pizza". When used as a consonant, = Y
j = not used in proper Latin--represents consonantal i and pronounced as Y
u = as in "doom" when a vowel, or as W when consonant. Properly written v.
v = u
Gaius = GUY-oos
Caesar = KAI-sar
provincia = pro-WINK-ee-ah
Vesuvius = wes-OO-wee-us
Adlocvtio = odd-low-COO-tee-oh
gladius = GLAH-dee-oos
pugio = POO-gee-oh (not POO-jee-oh!)
pilum = PEE-loom
caligae = CAH-lee-guy (not Caligula!)
Any other versions are bastardized by modern English. If you want the true to original Latin, spoken at the time of the conception of the Pilum; then this is it.
Keep in mind there are four ways to pronounce Latin, the reconstructed ancient Roman, the northern Continental European, Church Latin, and the "English method".
The above pronunciation guide uses the reconstructed ancient Roman method.
But hey, pronounce it anyway you like... ultimately, they all can be considered correct.