Taking down a conc block wall
Perhaps its the words you used or my lack of sleep during the last few days but I can't visualize what you are describing. Would appreciate if you can describe the inner cement basement wall again. thanks.
If this is a cement block wall down the center of the basement, it is most likely a load bearing wall. Load bearing from under basement floor (that has its own footings) to the upper floor joists. Do confirm if this cement block wall is load bearing or a simple boundary divider wall. This is very critical.
Also... If a person in a wheel chair plans to live in a basement, do contact your local building inspector. There's more the cement walls and doorways widths involved. There's emergency exists, bathroom customization, kitchen customization, etc. etc. All these areas must pass strict codes as well. Definately, well worth ensuring all areas are "wheel chair access friendly" as well...