How can I remove humidity from a room without a dehumidifier?
You can purhcase products such as DampRid. It is availabe in various size packages and will work to passively dehumidify a space.

You do not want to use a fan or any active air mover to attempt to dry the window space. This can enable the mold to spread to other areas.

Mold is dangerous to your health and this issue should be handled soon. One point of concern is that the mold may be in the drywall surrounding the window. The mold issue should be brought up to your building manager. If they do not take corrective actions, you should speak to the local public health department.