Non-religious Ceremony with a sprinkle of Jewish/catholic rituals

Unity candles are not Catholic at all, in fact most Catholic masses don't have any type of extra "unity" ritual. I would speak to your FH or his family as to what aspects they would like to see included. Suggestions might be playing the Ava Maria, or a prayer where the guests extend their hands towards the couple as a mass blessing.

ETA: If your dad is walking you down the aisle, I wouldn't have any type of "who gives the bride" verbiage because Catholics believe that the bride and groom give of themselves as consenting adults. Old tradition was for the man and woman to walk in together as a sign of their mutual desire to marry. It's only been in modern times that brides are escorted by their fathers, but they are not "given away".

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Thanks for your suggestions. I have spoken to FH and his family but they are at a loss as well, which is why I am coming here for suggestions! Both of my parents are walking me down the aisle, which is custom in Jewish weddings. I've never heard of a "prayer where guests extend their hands towards the couple as a mass blessing." Can you elaborate on that? Is there a certain blessing?

View Quoted Comment Nuptial blessings can be found here, you may want to modify to make less Christian. http://catholicweddinghelp.com/topics/text-nuptial-blessing.htm

We had a Catholic ceremony with a nuptial blessing. Husband isn't Catholic but not any other religion so the Catholic stuff was ok for him. Not sure if I would consider nuptial blessing something I consider representative of a Catholic ceremony...maybe the sign of peace instead?

Congregation extending hands in prayer Priest praying over couple Priest praying over couple 2

Catholic Nuptial Blessing

The nuptial blessing options can be found in the link above. The Officiant invites the congregation to join him in extending a hand to bless the couple as shown in the photos. If you find the blessings too religious or not inclusive of both faiths, any short prayer or blessing would do. It's just a nice touch to include your guests in the ceremony. I think it's awesome that you're trying to incorporate both faiths. Your tradition of both parents walking with you is awesome as well. Hope this helps - your officiant should also be able to help you create a ceremony that is perfect for you both. Happy Planning!

You could use the Catholic wedding vows. https://www.theknot.com/content/roman-catholic-wedding-vows