Keep qadha fast of Ramadaan during the first nine days of Zul Hijjah

I missed 10 fasts during Ramadan due to illness. I am recovered now and wish to complete my missed fasts. I planned to keep the 10 during the first days of Zil Hijjah not expecting any additional reward but just as a sense of fasting is more prevalent around me.

Please advise if this is ok as our local imam in a talk says Fardh and Sunnah cannot be combined! Should I rather wait and fast after or continue in these days? If I do fast, my intention is of my qadha and will I be in sin for keeping these qadha in the auspicious days of Sunnah fasting?