I want to complete reading the Quran (khatm) during the month of Ramadhan however I am unsure about rulings whilst menstruating. I am aware I can recite the Quran but can not touch the writing however what do I do about compulsory sujoods? Can I perform them without wudhu during menstruation? Or will I have to skip those ayat out and not be able to complete the Quran fully

Leave those Aayat and read later when you will be in the state of taharat and then perform the sajda.
Recitation of more than 7 verses without touching Quran itself is makrooh therefore complete the Quran when you will be in the taharat and in those days you may recite tasbeeh and do Zikr.