From the Theological Dictionary of the Old Testament, we see that Tammim comes from the root tmm, used throughout the ANE (both semitic and Egyptian) with meanings of "come or bring to an absolute end".
From this, the word when used as a noun or adjective, it would mean fulfilling one's purpose or design perfectly/completely/fully, but when used as a verb it could mean to "utterly destroy" or "brought to a complete end".
A specific case of the noun-adjective form is in cultic practices (e.g. animal sacrifice, priestly rituals) where it means "unblemished":
with very few exceptions, the verbal forms denote the observable fact
that something has come or been brought to an end (often with negative
connotations), whereas the noun and adjective (apart from the cultic
term tāmîm describing a sacrificial animal as “unblemished”) belong to
the psychological and moral realm and refer to the positive attribute
of “uprightness.” This observation explains why the nominal forms
appear primarily in wisdom literature and texts influenced by it.
The broad semantic range can be attested by LXX translations of this word:
For the subst. form tāmîm (tām) with its positive connotation, the LXX
generally uses forms with an alpha privative. The adj. ámōnos,
“without blemish” (ca. 50 instances)—supported by Lev. 22:21: “(the sacrificial animal) must be perfect [Gk. ámōnos]; it shall have
no blemish [meʾum; Gk. mṓnos]”—can also denote moral
blamelessness. Other, less common, privative forms refer only to the
latter and appear primarily in theological texts that deal with
ethical conduct (Psalms, Job, Proverbs): ákakos, “innocent” (ca.
15 instances); ámemptos, “blameless”; athaṓ̧s, “not subject to
prosecution.” Among the nonprivative forms, the most common is téleios
(7 times), which means “perfect” in both the physical and the moral
sense; others include hósios, “devout” (5 times), katharós,
“pure” (bis), díkaios, “righteous,” and alēthinós, “true.” All these translations emphasize various nuances of the Hebrew root.
In the case of Ezekiel 28.15, it is an adjective, and "perfect", "blameless", "righteous", "guiltless" would all be reasonable translations as the word has a broad semantic range.
Kedar-Kopfstein, B. (2006). תָּמַם. G. J. Botterweck, H. Ringgren, & H.-J. Fabry (Eds.), D. E. Green (Trans.), Theological Dictionary of the Old Testament (Revised Edition, Vol. 15, p. 700). Grand Rapids, MI; Cambridge, U.K.: William B. Eerdmans Publishing Company.