Briefly: Yes, you can change the ballot to a different party in the booth.
In Sweden sometimes you get ballots in the mail from parties eager to gain your vote. There are also ballots in the voting place.
You pick these 'publicly' from a stand and it is normal to pick many of them and bring several into the voting station (behind curtain) and then pick privately among them. You can leave the ones you don't use in there or put them into your pocket. You leave the voting station with a sealed envelope with the real ballot in it. This is your vote.
If you are in company of a nosy family when picking the public ones, consider preparing, and bringing a blank one covertly writing your desired party in the voting station. The pre-printed ballots are mainly there for convenience. A friend working in voting place said they are lenient when interpreting handwritten ones, take that for what it is. If the opportunity presents itself you can visit the voting place without company and take the appropriate ballot in advance.
From the official page if you by 'changing' mean 'manipulating the ballot':
Valid ballot papers
A ballot paper is valid if it contains a party name the party has notified its
participation in the election. It can be a name ballot paper, a party ballot paper or a blank ballot paper on which the voter has written a party name.
New routines from 2018 (official video explainer of how to set up a voting place, in swedish) instructs to make the area where you pick your ballots more covered. I do not remember this from 2018, but if your voting place is up to date with these new routines you should be able to pick from the ballot stand in privacy from your family.
Clarification (from comment by Guran): If you pick a ballot paper for Party A and (behind the screen) cross out "Party A" and clearly write "Party B", that will count as a valid vote for Party B.