I think - as a teacher who has worked part time and full time, and has taken children on residentials many times - it would be entirely reasonable to say that you can only attend the residential on your normal days.
What is your jobshare partner planning to do? If they are attending full time, then a reasonable option for both of you - at no cost to the school - would be for them to be ‘full time’ for the week of residential, and you to cover their days in addition to your own on another week (either as a block or as individual days). You may well be most successful with senior management by presenting this solution together.
If, on the other hand, you are both being expected to go full time (as residentials typically require higher staffing ratios than a normal school day), then it is reasonable to ask for additional pay, or toil, or to say that you cannot go but will of course cover the class of a full-time member of staff from another year group for your normal days so they can go at lower cover cost for the school.
Or, if some pupils don’t go on the residential, you can volunteer to run the activities in school for them during your normal working days.
It’s difficult because you’re new to the school, and will not have established a reputation or working relationships as yet. There is no urgency - staffing for the residential will not be finalised until the Summer term - so for the moment I would concentrate on settling in, establishing a good working partnership with your jobshare, getting a reputation for being a good, hardworking teacher. From that foundation, it will then be much easier to make requests and suggestions about the residential closer to the time.