Can I Marry Without a Wedding?

I am not entirely sure what you mean by “wedding.” I will assume you mean that you do not want a full nuptial Mass. In that case, there are a few options:

• A Liturgy of the Word with the exchange of vows. This is the usual choice when one spouse is not Catholic.
• Exchanging vows at any regular parish Mass. I have seen couples exchange vows at a regular Sunday or daily Mass.
• A simple exchange of vows and reception of the marriage blessing with nothing else. This is rare but not unheard of.

If the marriage is between two Catholics, the normative expectation is that the exchange of vows will take place within Mass (Order of Celebrating Matrimony, 29).  In this situation, you would need to explain to the priest your reasons for not wanting to exchange vows during a Mass.