Is there a Prophetic Hadith with the wording: "The day of your fasting is the day of your sacrifice" or something similar to it?

This wording has no basis. Al-Harawi mentioned it in (Al-Masnu' fi Ma'rifat Al-Hadith Al-Mawdu') and attributed it to Imam Ahmad. Muhammad ibn Abi Bakr Az-Zar'i stated in (Naqd Al-Manqul) that it is among the false hadiths. Al-'Ajluni in (Kashf Al-Khafa') attributed it to Ibn As-Salah, who in turn attributed it to Imam Ahmad.