Jonathon Green, Cassell's Dictionary of Slang, second edition (2005) has a couple of entries for cleanskin and clean skin:
cleanskin n. (also clearskin) {1940s} (Aus./N.Z.) 1 a person without a criminal record. 2 An honest person, esp. in politics. {S[tandard] E[nglish] cleanskin/clearskin, an unbranded cow}
clean skin n. see LILYWHITE n.3 (2) [identified elsewhere in the dictionary as U.S. slang, dated to the 2000s, and defined as "a drug trafficker who deliberately eschews ostentation to maximize their chances of avoiding arrest"].
These entries indicate that while cleanskin is a term used primarily in Australia and New Zealand, a similar term clean skin may have arisen in or migrated to the United States, albeit in the narrow sense of a drug trafficker who avoids attracting attention through a flashy lifestyle.
Tom Dalzell & Terry Victor, The New Partridge Dictionary of Slang and Unconventional English (2006) offers four definitions of cleanskin, all from Australia and none involving actual tattooing (or the absence thereof):
cleanskin noun 1 a person without a criminal record AUSTRALIA, 1943 Originally applied to an unbranded sheep. [citations omitted] 2 a novice AUSTRALIA, 1907 From the conventional sense (an unbranded stock animal). [citations omitted] 3 a person of integrity, especially in a political context AUSTRALIA, 1942 From the sense of 'a person without a criminal record'. 4 In horse racing, a jockey who has never been disqualified in a race AUSTRALIA [citation omitted]
As recently as the turn of the century, Macquarie Slang Dictionary, revised edition (2000) did not mention "untattooed person" as a meaning of cleanskin:
cleanskin n. 1. Originally. an unbranded animal. 2. one who is free from blame, or has no record of police conviction.
Similarly, G.A. Wilkes, A Dictionary of Australian Colloquialisms, fourth edition (1996) lists only two meanings for cleanskin:
cleanskin 1 An unbranded beast [First cited occurrence:] 1881 A.C. Grant Bush-Life in Queensland i 206: These clean-skins, as they are often called, to distinguish them from the branded cattle, are supposed to belong to the cattle-owner on whose run they emerges from their shelter. 2 A person without a police record [First cited occurrence:] 1907 Alfred Searcy In Australian Tropics 112: The men I met with were good, honest, and hard working, although perhaps it might have been as well for a clean skin to fight shy of some of them.
Assessment
As of 2005–2006, "untattooed person" was evidently not a recognized meaning of cleanskin in major slang dictionaries published outside Australia and New Zealand—and as of 1996–2000, it appears not to have been a recognized meaning in major slang dictionaries published in Australia. Any proliferation of the meaning beyond Australia and New Zealand must therefore have occurred quite recently, if at all, given how recently it emerged there.