Any high detergant oil will do. I use air tool oil. It wicks in very tight spaces. I remove the FW. Put is upside down on a dirty rag, and drip oil from the back side.
The oil and dirt will flush out from the front.
This way you are flushing dirt out.
You can also drip it from the front if you don't have the tool to remove it which was also mentioned.
Now that it is working, I wouldn't worry about it too much. When you are pedal backwards there is not much stress on the Freewheel.
If you do own a vise, I would recommend you buy the FW removal tool. Sooner or later you would need it to clean or replace the FW.
Enjoy the Centurion Ironman. They are great bikes and we have a few experts here on them.