Though there's a reference for morning netilat yadayim within the Zohar, is it a rabbinic decree, or a Torah based mitzwot for ALL Yisrael outside of the kohenim?
Netilath yadayim in the morning as a preparation for prayer is derabanan (rabbinic). The Talmudic source for it is the statement of R. Yohanan (and R. Yohanan as cited by R. Hiyya b. Abba) in Berakhoth 14b-15a:
אמר רבי יוחנן הרוצה שיקבל עליו עול מלכות שמים שלמה יפנה ויטול ידיו ויניח תפילין ויקרא ק"ש ויתפלל וזו היא מלכות שמים שלמה א"ר חייא בר אבא א"ר יוחנן כל הנפנה ונוטל ידיו ומניח תפילין וקורא ק"ש ומתפלל מעלה עליו הכתוב כאלו בנה מזבח והקריב עליו קרבן דכתיב (תהלים כו ו): "ארחץ בנקיון כפי ואסובבה את מזבחך ה'"
R. Yohanan said: If one desires to accept upon himself the yoke of the kingdom of heaven in the most complete manner, he should consult nature and wash his hands and put on tefillin and recite the Shema' and say the tefillah: this is the complete acknowledgment of the kingdom of heaven. R. Hiyya b. Abba said in the name of R. Yohanan: If one consults nature and washes his hands and puts on tefillin and recites the Shema' and says the tefillah, Scripture accounts it to him as if he had built an altar and offered a sacrifice upon it, as it is written, I will wash my hands in innocence and I will compass Thine altar, O Lord.
He specifies that this practice, as performed alongside other miswoth has the effect of cultivating acceptance upon ones self of the yoke of heaven in the most complete manner.
Insofar as our source for the practice is R. Yohanan, the practice is rabbinic. This is confirmed in many other sources. For example, the Rambam explicitly states (H. Berakhoth 6:2):
כל הנוטל ידיו--בין לאכילה, בין לקרית שמע, בין לתפילה--מברך בתחילה, אשר קידשנו במצוותיו וציוונו על נטילת ידיים: שזו מצות חכמים היא שנצטווינו בתורה לשמוע מהן, שנאמר "על פי התורה אשר יורוך" (דברים יז,יא).
Whenever a person washes his hands - whether before eating, before the recitation of the Shema', or before prayer - he should recite the following blessing beforehand: "[Blessed are You...] who sanctified us with His commandments and commanded us concerning the washing of hands." This is a Rabbinic miswah that we have been commanded by the Torah to follow, as [Deuteronomy 17:11] states: "[Do not stray...] from all the laws that they direct you."
Mishneh Torah, Brachos, chapter 11; halacha 3:
"Similarly, with regard to all the Rabbinic mitzvot - both the mitzvot that the Rabbis established as obligations - e.g., reading the megillah, lighting Shabbat candles, and lighting Chanukah candles - and the mitzvot that are not obligations - e.g., an eruv or washing hands - one should recite a blessing before performing them, [praising God] "who has sanctified us with Your commandments and commanded us….”"
It's clear from this paragraph that washing one's hands is rabbinical in nature.
Ramban (Nachmanides) writes in his commentary on the pasuk "You shall be holy":
It is with reference to these and similar matters that this general commandment [Ye shall be holy] is concerned, after He had enumerated all individual deeds which are strictly forbidden, so that cleanliness of hands and body, are also included in this precept, just like the Rabbis have said: “And ye shall sanctify yourselves.10 This refers to the washing of hands before meals. And be ye holy. This refers to the washing of hands after meals [before the reciting of grace]. For I am holy — this alludes to the spiced oil” [with which they used to rub their hands after a meal]. For although these [washings and perfuming of the hands] are commandments of Rabbinic origin, yet Scripture’s main intention is to warn us of such matters, that we should be [physically] clean and [ritually] pure, and separated from the common people who soil themselves with luxuries and unseemly things.
However, see the Gemara in Chullin 105a:
§ Having mentioned the manner of washing hands during a meal, the Gemara discusses another matter concerning washing hands. Rav Idi bar Avin says that Rav Yitzḥak bar Ashyan says: The first waters, i.e., washing of the hands before eating bread, are a mitzva by rabbinic law, but the final waters, washing of the hands upon conclusion of the meal and before reciting Grace after Meals, are an obligation, a more stringent requirement.