import pywikibot
from pywikibot import pagegenerators

site = pywikibot.Site('commons', 'commons')
cat = pywikibot.Category(site,'Category:Hand-powered_beaters')
gen = pagegenerators.CategorizedPageGenerator(cat)

for page in gen:
    text = page.text
    if "egg" in page.text.lower():
        print(page.title())

File:Beater, egg (AM 69958-2).jpg
File:Dover Eggbeater.jpg
File:Eggbeater stencil.svg
File:Eggbeater, Pictorial Equipment Article, Kellogg. (3856709638).jpg