First, I hope you do not have that many word sections. "Section," in Word jargon is a particular part of a document. Every document has one and can have many. Each additional section adds quite a bit of formatting complexity to the document.
Sections / Headers and Footers in Microsoft Word (Ribbon Versions)
Footers are a part of Section formatting.
I would suggest using field coding using a conditional
IF Field. That field could give you one footer if you are not on page 10 and a different one if you are on page 10. The field is in the footer "story."
{ IF { PAGE } <> "10" "Footer for all pages other than 10" "Footer for page 10" }
The braces cannot be typed, they must be inserted using Ctrl+F9 or otherwise by Word directly.
The easiest solution is to probably put a section break before page 10 (perhaps a "next page" section break) and another at the bottom of page 10. Then make the footers for both not linked to previous and then change the footer on page 10. While this is the easiest, it results in a more complex document. The field solution is a bit of trouble to set up but gives a less complex document structure.