All perfect praise be to Allah, the Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
There is no relation, at all, between observing Ramadan’s compensatory fasts and removing the hair which one is commanded to remove from the body. So you should hasten to make up for the fasts that are due on you before the advent of the next Ramadan; and your fast is valid even without removing the hair which is recommended to be removed.
Moreover, you should know that there is no difficulty in removing such hair since there are many ways to remove it, praise be to Allah, all of which achieve the purpose. It is permissible for you to remove it by plucking or by shaving or by using hair removers. You should not leave the hair of the pubes, the armpits, etc. which one is not allowed to grow for more than forty days, as stated in the Sunnah.
Allah knows best.