I was learning something related in the Sefer Vezos Haberacha (וזאת הברכה) and came across this exact case!
He writes (in Perek 13, in the context of discussing cases that are exceptions to general rules of "ordering of brachos") [loose translation by me]:
וכן אדם שבא לאכול סעודה, ורוצה להקדים ולשתות לפני הסעודה, מפני שהוא צמא, רשאי לעשות כך אף שמברך ׳שהכל׳ לפני ברכה אחרת יותר חשובה, כי כך הוא סדר הדברים למי שצמא (פה״ל פ״ה הע׳ ד׳
And also someone who wishes to eat a meal, but first wants to drink because he is thirsty, is allowed to do so even though he is saying Shehakol before any other beracha which may be more chashuv - because this is the normal procedure for someone who is thirsty.
So, in short, you are allowed to make a bracha on the cup of water first.
His source appears to be the Sefer פתחי הלכה by Rabbi B. Forst (who is also of The Laws of B'rachos fame). However, I was unable to find this exact case in either of his Seforim. He does however discuss (which is also brought in the Halachos of Brochos by Rabbi Bodner) the general exception to the ordering of brachos in cases where there is a specific reason for changing the order (the example given, if I recall correctly, is having the appetizer before the main meal, where normal brachos rules would dictate otherwise).
I also want to point out that this last novelty is said even in a case where both foods are directly before him. For if not, the rules would allow him to say the bracha on that which is before him, and not require him to go and retrieve the other item.