I wouldn't get into SSPX issues with the pastor. The only thing you need to make clear to him is that your previous chrismation/confirmation is valid. The Catholic Church teaches that confirmation/chrismation can only be received once, and it would be sacrilegious to attempt to repeat it. I really would urge you to contact a Byzantine Catholic pastor, because he will understand the issues involved. You should be received into the Catholic Church by a profession of faith alone, according to Catholic canon law. Here is the relevant citation from the Code of Canons for the Eastern Churches:
A member of the Christian faithful of an Eastern non-Catholic Church is to be received into the Catholic Church with only the profession of the Catholic faith, after doctrinal and spiritual preparation according to each one's condition.
It actually might be less of a hassle if the Ukrainian Catholic pastor receives you into the Church. If he does, however, I do not think that you will belong to his jurisdiction canonically. A convert from the Greek Orthodox Church becomes a Byzantine Catholic canonically, but, because there is no Hellenic Greek Catholic jurisdiction in the U. S., I believe that you would be a subject of the local Latin bishop, as are, e.g., the Italo-Greek Byzantine Catholics in New York:
Of course, after your reception into the Catholic Church, you are free to attend any Catholic church of any rite. However, it may be important for canonical reasons to know that you are a Byzantine Catholic.