I realize it’s probably too late to be helpful, but if anybody else comes upon this question, I’ll add my answer from experience. A growler will keep for a few weeks if unopened and filled to the top, as long as the cap is tight and sealed well.
Once you open it you really only have a day to drink it, maximum. I personally have left growlers unopened for a few weeks and they have tasted perfect when I finally got to drinking them. I know people who have left growlers for months, with little to no ill-effect.
Yes, a wheat beer can be a slightly more delicate beer style, but it should last perfectly fine for a week in an unopened growler.
And, as an aside, almost all wheat beers are brewed with ale yeast, not lager yeast… although this won’t have a huge effect on how the beer lasts, you should worry more about the amount of alcohol and how flavorful the beer is. There are many lagers that are very strong and flavorful and many ales that are light and delicate.