When performing Kaparos over money should it preferably be done by the time of Ashmuros Haboker, as applies when doing Kaparos over chickens?

Even when doing Kaparos over money, it should be done specifically on Erev Yom Kippur as recorded in the Shulchan Aruch regarding the regular Kaparos. However, regarding if it should be performed towards dawn by Ashmuros Haboker, seemingly this is only relevant to when Kaparos is done over a chicken, and thus if waking up this early can ruing ones schedule of Davening, learning or other matter of Avodas Hashem, it should be done later on, on Erev Yom Kippur rather than Ashmuros Haboker, when doing over money.[1]

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[1] Explanation: The source of doing Kaparos over chicken at the time of Ashmuros is from the Arizal, and is later recorded in the Siddur of Admur. It is clearly implied from their wording that the main idea is to have the chicken slaughtered at that time, which would imply that if one is not doing it over a chicken, or if it will not be slaughtered then, then there is no reason to do it specifically by dawn. They explain that the slaughtering of the chicken by Ashmuros helps sweeten the severities and the time of Chesed is by Ashmuros Haboker, and hence it helps to sweeten the severities. Nonetheless, one can argue that there still remains some advantage of doing Kaparos over money then, as certainly giving charity likewise sweetens the severities. This would however then enter into the question of giving charity at night before dawn etc which some are particular ion [but not Chabad which allows giving charity after midnight], as well as that I have never heard of Kaparos over money needing to be done before Alos, and hence I would conclude as above. [See Admur 605:1; Siddur Admur; Arizal in Peri Eitz Chaim Shaar Yom Kippur 1]