Using a Greek Lexicon, I was able to find that this same word is used in the Septuagint (LXX). This passage makes it seem that it is not offensive (Ecclesiasticus – Sirach):
27:4 As when one sifteth with a sieve, the refuse remaineth; so the filth of man in his talk.
27:4 ἐν σεισματι κοσκινου διαμενει κοπρια οὑτως σκυβαλα ἀνθρωπου ἐν λογισμω αὐτου
The word means excrement or dung, which are polite and respectable words for offensive things which people, when bitterly cursing in anger, naturally refer to.
To make the case that Paul uses profanity, or even a word that would offend others, would require more examples with more positive proof, especially considering that Paul opposes profanity:
Let there be no filthiness nor foolish talk nor crude joking, which are out of place, but instead let there be thanksgiving. (Ephesians 5:4 ESV)
Paul also emphasised avoiding things that offend a brother, like meat sacrificed to idols (1 Corinthians 8:13). Therefore it is difficult to imagine he broke his own rule publicly, especially in a writing to the churches. For Paul to use a crude or offensive word would then be out of line with Paul's own imperatives.
If Paul used offensive language, he would have detracted from the argument that he was making. What Paul was saying is that righteousness based on the law was a human work that needs to be expelled with absolute prejudice, naturally lending itself to the concept of human waste. Indeed, in his mind righteousness by works was to be expelled from the body and put somewhere disgusting without touching it with one's hands. He intended to make one feel righteousness of the law as loathsome. To bring attention to himself by a obscene or offensive word would detract from the shock of the idea that everything we do in dedication to God, if without faith, is disgusting. The reason why he searches for an idea so revolting, like human waste, is because he wants the reader to understand how necessary the free gift of salvation through Christ's atonement is. Everything else must be expelled into a toilet. In this way inoffensive words present a clear, possibly offensive, doctrine.
To be thorough, I looked up the word in arguably the most famous, exhaustive and academically authoritative book on biblical Greek definitions. Here is what I found in his final conclusion after many pages of evaluating many references in Greek writings:
The two elements in σκύβαλον, namely, worthlessness and filth, are best expressed by a term like “dung.” (Theological Dictionary of the New Testament, Gerhard Kittel, Volume 7, 447)