Hi!
First of all, huge congratulations on securing the scheme and on graduating - both are amazing achievements!!
I don't think attending your graduation for one day should materially harm your chances, especially as you have already been transparent with the graduate recruitment team and they have encouraged you to go. If they thought that it would seriously impact your prospects, I imagine they would have been much firmer about attendance.
This is also probably more common than you think (though firms may have different policies on it), particularly for summer schemes. On some of my schemes last summer, there were people who had a day away to attend their graduation (as it usually falls in the middle of summer schemes), so firms are definitely used to dealing with this situation.
The main thing is to just make sure that you handle it professionally - for example, giving plenty of notice, staying engaged, and making an effort to catch up on anything you miss. In the grand scheme of things, your overall performance and attitude across the scheme will matter much more than one day of absence for an important life event!
I also think it is important to consider whether you would regret missing your graduation later on, especially when the firm has already shown understanding and flexibility in relation to the situation.
Wishing you the best for both the vacation scheme and graduation - hopefully you'll be able to celebrate two things this summer!