Your question deserves a serious response. The issue of a Jewish wedding to be conducted on the holy Shabbat, is raised frequently by Jews such as yourself, who are not Sabbath observers. This, of course, is a touchy subject.
You have referred to your father's Judaism as "orthodox" and that he would not be attending your forthcoming wedding as it would be "sacrilegious and would violate the sanctity of Shabbat."
While the term or title "orthodox" is often employed by non-orthodox Jews as a way of characterizing other Jews, as perhaps over the top or unreasonable, it really is a term that means to be observant, or taking seriously the covenant - 'b'rit' - with the God of Israel. This means adherence to God's Torah and Mitzvot - Holy Scripture and Responsibilities or Commandments.
Your dad's refusal to attend your wedding - hatunah - if held on Shabbat is, of course, painful for you, but also painful for him and your future bride.
Let's look at the matter from the standpoint of values,priorities and standards. One who adheres to a lifelong commitment to what is understood as a relationship of devotion to God and His commandments, is to be seen as having an unswerving dedication to upholding his own part of the bargain.
When driving an automobile, you will see posted the speed limit sign. If the state or municipality has posted 50 MPH and you drive 70 MPH, a police officer can pull you over and write a ticket, since you have disobeyed the posted limit.
Shabbat, as you clearly understand, stands for a special relationship between the Jew and his/her God. The Jew must ask himself/herself whether this or that is permitted within the parameters of Sabbath observance. This is not defined by the Jew, rather it is handed down to us from above.
You have asked for a Scriptural reference for a wedding prohibition. As you may know, our Judaism is not Scriptural Judaism, rather it is Rabbinic Judaism. This is complex and often not understood by the uninitiated. It is the Judaism as handed down to us through the Oral Tradition of Torah. Thus, every verse in the Written Torah -Torah she-b'khtav - is interpreted by the Oral Torah - Torah she-b'al peh.
Does this mean that the Torah as taught by the Sages of Israel - the Hakhamim - is more important to us than the Written Torah? Well, in a word, yes. We do not understand our Torah without the filter of our Rabbis' teachings.
Even if we cannot find an explicit verse or phrase in the Torah that refers to a prohibition of conducting weddings on Shabbat, we will still follow the time honored traditions handed down by the Sages of Israel.
Let's look at a familiar rabbi's manual in Hebrew and English, known as Hamadrikh -- The Rabbi's Guide, by Hyman E. Goldin, c. 1939. The manual cites sources from the Talmud Bezah, Talmud Moed Katan, Maimonides' Code- Mishneh Torah and the Shulhan Arukh -Code of Jewish Law, "It is forbidden to perform the wedding ceremony on the Sabbath, Festivals, and on the Intermediate Days of the Festivals." (p.6)
All rabbis adhering to Jewish Law - Halakhah- will take this seriously and will not conduct a wedding in contravention of the Halakhah.
Since it seems that the real issue that you present deals with your father and the concern that you have for his refusal to attend your forthcoming wedding, it is obvious that you would be pained by your father's absence on such a momentous occasion in your life and that of your fiancé and other family members.
For this reason alone we need look no further in the Torah than what we know as the Ten Commandments or Decalogue -Asseret Ha-dibberot. (Exodus 20:12) The fifth commandment of the 'Big Ten' says, "Honor your father and mother. You will then live long on the land that God your Lord is giving you."
It is unusual to find a commandment in Torah that states a reward for its observance, but in this case the Torah is quite explicit that one is well rewarded with life for demonstrating respect to one's parent.
Honoring the holy Shabbat and honoring your parent will only bring blessing. There is no downside.
Here is a wish that you make the right decision in respect of the Shabbat and your father.
Wishing you Mazal Tov!