Jacobite girl and Catholic Boy (Syro-Malabar) marriage and inter-liturgy (Can we have Syro-Malankara mass in Syro-Malabar church)

I was thinking about the marriage between a Syro-Malabar boy and a Jacobite girl. I know there are norms and rules about marriage between people from both churches and it is allowed. But the girl has a weird request as the boy is Syro-Malabar the wedding will be in a Syro-Malabar rite but in the Syro-Malabar rite in the wedding ceremony, the bride and groom are required to place hands on the holy gospel and take an oath. She is against taking an oath as she claims it is a direct violation of the commandment "Thou shalt not take the name of the Lord thy God in vain". This has quite stirred me as the oath-taking is done by placing hands on the Bible. To solve this I found a solution to change from Syro-Malabar to Syro-Malankara as in Syro-Malankara it is different and more familiar to the girl and no bible- and oath-taking (correct me if I'm wrong). But the problem is there is only one Syro-Malankara church nearby and it is far away from the boy's Parish which can create logistical and other problems as both of them have a big family and related issues. I was wondering if there is any way to conduct a Syro-Malankara rite at the Syro-Malabar church (boy's Parish). I also would love to know any other potential solutions. As she was brought up in her faith I cannot force herself to correct it (I don't have the authority). And I want to respect her beliefs also don't want to create a problem. Would it be a problem if she didn't hold the Bible and take an oath?