No. It's okay to leave out "有", but "了" signifies a completed action, so you can't tack it on to something you haven't yet done. You could use "呢" instead (I believe, subject to correction by a native speaker), but you don't have to.
This is very colloquial and I'm not sure how many people actually say this, but you can use 淋个水 or 冲凉 or 洗澡, usually the last is a long bath, the first is a quick shower and 冲凉 can be for either.
If you want to take a hot/cold bath it's 泡热/冷水澡.