Origin of the phrase Sica
I'm confused. You claim, "[t]here is no attested connection between the Albanians and Illyrians," yet the w:Proto-Albanian language and w:Albanian language articles both mention a likely derivation from Illyrian. Are you claiming that both of these articles are incorrect? Or are you trying to claim that the lack of attestation of a connection is proof that there is no connection?
You also claim, "the phrase 'Thika' derives from the phrase 'Sica'", but Albanian diachronic sound patterns do not seem to bear this out. A quick survey of the Albanian lemmata here on Wiktionary shows that ⟨th⟩, /θ/ derives most commonly from PIE /k/, with occasional instances of shifts from alternative Albanian terms with initial ⟨f⟩ instead (not surprising, phonetically; observe the opposite /θ/ → /ɸ/ shift in certain dialects of English). The only clear cases where Albanian initial /θ/ comes from an earlier /s/ phoneme were theks (“to say”) from Proto-Indo-European *sokʷ-o-, and thi (“pig”) from Proto-Indo-European *suHs -- but in both cases, the vowels are back vowels, not the front /i/ vowel in thikë.
Meanwhile, many modern Albanian terms starting with ⟨th⟩, /θ/ are proposed to derive from earlier forms starting with ⟨ts⟩, /t͡s/. Latin lacked this phoneme, making a shift from /t͡s/ to /s/ a likely adaptation for borrowed terms -- more likely than the proposed /s/ → /t͡s/ shift for a borrowing from Latin into Albanian.
Your insistence on a possible Slavic origin for the Latin term sica is also puzzling, as the term is attested in Roman sources two millenia old, whereas the Slavs didn't migrate west until the 5th and 6th centuries. Unless you are also positing that the Slavs were either time travelers or common tourist visitors to the Illyrian coast, any Slavic derivation is geographically unlikely.
De Vaan aside, your case is not convincing.