How can I sue in Small Claims Court a New York company, if I'm a LLC in United Kingdom?

You can have a lawyer represent your llc (in fact, as a general matter you can't represent the llc unless you are an attorney, although some small claims courts may allow it) but (a) it will probably cost as much or more than your travel expenses and (b) you would have no way of proving your case, since the attorney would have no knowledge of the facts other than what you had told him.  You need a witness with knowledge of the facts to testify.  Even if your case is based on documents, you will need someone to authenticate the documents. Why don't you sue him/her/it in England?  British law may be different, but if it is similar to American law in this area, the British courts would have jurusdiction over the defendant since the suit is over a contract he/she/it entered with a British resident which involved he/she/it remitting money to England and/or returning goods to England.  Once you obtain a judgment, you will probably have to domesticate the judgment in NY to collect, but all you would have to prove is jurisdiction.  If that was satisfied, you wouldn't have to establish the merits again.