See Shulchan Aruch OC 4, 7:
טוב להקפיד בנטילת ידיים שחרית בכל הדברים המעכבים בנטילת ידיים לסעודה.
הגה: מיהו אינו מעכב, לא כלי ( מגן אברהם: פירוש, בדיעבד היכא דאי אפשר בעניין אחר; אבל היכא דאפשר, טוב להקפיד) ולא כוח גברא ושאר הדברים הפוסלים בנטילת הסעודה (מרדכי ריש פרק אלו דברים, תשובת רשב"א סימן קצ"ה).
Bet Yosef:
וכתב רבינו ירוחם בנתיב י"ו חלק ו': ומברך "על נטילת ידים", על שם הכלי שנקרא אנטל. ואף שלא נתקן הכלי אלא בשביל נטילת האכילה, מכל מקום לא ישנה הברכה. וכן כתב הרא"ש
A vessel was instituted by Chachamim for washing of meal only. But Lechatechilla, the SA (based on a deduction from the words of the Gemara by the Shut Harashba (¹), and according to the Zohar) says that its good to make a point to take a vessel. But it is not meykar Hadin. The nusach of the blessing itself makes allusion to the vesssel which is called natla. Bet Yosef makes the same deduction from the Gemara Berachot 15a
he should heed the call of nature and wash his hands ("ויטול ידיו") and put on tefillin and recite the Shema' and say the tefillah:
In Shulchan Aruch and commentators on the page(¹), nobody needs vessel bediavad and everybody advised to use vessel lechatechilla.
See SA OC 232, 2:
אם יש לו מים וצריך ליטול ידיו כדי להתפלל אף על פי שאינו יודע להם שום לכלוך ולא יברך (יזועיין לעיל סימן צ"ב סעיף ה').
הגה: ואפילו עומד מלמודו יטול ידיו יטלתפלה (מנהגים).
ואם אין לו מים מזומנים כאינו צריך ליטול:
It is true for Mincha and Arvit too.
(¹): Thanks to @Avrohom Yitzchock I added this note:
Someone asked the Rashba (the Shut is quoted in Bet Yosef here) about the fact that the blessing for washing of the morning mentioned a vessel (natla) when the halacha doesn't require this.
Rashba answered with four arguments:
The custom everywhere is to wash with a vessel fulfilling the same conditions required for washing before a meal.
Gemara in Chulin says that washing of morning can be useful for the subsequent meal, and for meal we need a vessel, so the morning washing is also made with a vessel.
Gemara uses different expressions for the washing before morning prayer and the washing before Shabbat. The verb "notel" used for the morning washing refers to the vessel used.
The specificity of the washing of morning prayer is linked to the fact that Chachamim made a special blessing for this washing. A washing with a blessing of asher kiddeshanu is a mitsva derabanan statuted "כעין דאורייתא " (similar to washing which are mitsvot of Tora) i. e. similar to kiddush Yadaym of Kohanim, which requires a vessel.
So, for Rashba maybe that the blessing of netilat yadaym requires not only lechatechilla, but perhaps even bediavad, a vessel.
Anyway, the OP was asking for an opinion that allows without vessel at all even lechatechilla. For now I have not found such opinion in Acharonim (regarding netilat yadaym of mornings prayer). But Rabenu Yerucham, the Rosh, the Hagahot Mordechai and the Ran didn't need keli, even lechatechilla even for Shacharit.
Note: All this issue regards the washing before morning prayer but for Mincha and Arvit I didn't find someone who needs a keli lechatechilla. The unique reason to require a vessel for morning prayer netilat is the text of blessing according to the Rashba. Last opinions are more lenient than Rashba regarding the lechatechilla of the netila before Shacharit, a forciori regarding Mincha and Arvit.