It can be said either way: the variation is related to a general pattern of variation in the pronunciation of the final unstressed vowel in words such as happy. American English speakers and many British English speakers pronounce the final syllable of happy with an "EE" sound, but some British English speakers pronounce it with an "IH" sound. See this blog post from the phonetician John Wells: happY again," John Wells's Phonetic Blog, Thursday, 7 June 2012.
Anyone who pronounces the "happy" vowel as IH will presumably also pronounce the vowel in oxymoron as IH. For someone who pronounces the "happy" vowel as "EE", I think it would be most common to use that same vowel in "oxymoron" due to it being thought of as a compound or prefixed word (composed of "oxy" + "moron").
Wells doesn't mention oxy- in particular, but he does sat that "certain word-like combining forms such as poly-" end in a vowel that has the same variable pronunciation found in happy.
Wells describes the "IH" pronunciation of the happy vowel as "the traditional RP lax vowel" and I have the impression that even though it still exists in British English, it has become old-fashioned and less common than the "EE" version. The phonetician Geoff Lindsey writes:
Some older RP speakers (including John [Wells] himself, b. 1939) still have KIT /ɪ/ in happy and coffee, but this was already sounding old-fashioned in the 1980s, and today it’s frankly absurd to suggest to learners that opportunity, charity etc. should be pronounced in some way that’s different from the FLEECE vowel.
("The fallac[ɪj]of schwee", Speech Talk, June 21, 2012)
I guess it might be possible to hear the "IH" vowel for some people who have "EE" in happy, but that's probably uncommon as well.