Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Dear brother, if you want to enter a mosque for some good will and useful purpose then you are allowed; there is no impediment in doing so.
It is also permissible to enter a mosque wearing shoes if they are free from impurities particularly in your case since you are unable to remove them for a physical reason. If someone objects to your entering, you may explain to them the permissibility of this act.
However, we would like to inform you that though it is permissible but if it causes any dispute, harm, disagreement then it is recommended that it be avoided.
Allah knows best.