For some baffling reason, all the tertiary weapons have a separate key binding despite there only being three weapon slots. Ordinarily, one would go into the options menu and bind all of the weapons to the 3 key to have the weapon selection operate as expected, but this, unfortunately, does not work. Instead, you'll have to dive into and manually edit a config file.

NOTE: YOU MUST REBIND THE WEAPON KEYS IN ORDER FOR THE CONTROLS.XML FILE TO DISPLAY THE LINES WE NEED TO EDIT.

Right-Click on Bionic Commando and select "Properties."
Go to the Local Files tab and select "Browse Local Files."
Open the data folder then the settings folder.
Right-click on controls.xml and select Edit. This'll open up Notepad.
Press Ctrl+F to bring up the Find Window and type "equip".

You should see a line of text like this:
<button_name="equip_tarantula" input="6">

Replace the number with 3 and select Find Next in the Find Window.
Repeat this process for every weapon except the pistol and grenade.
Close Notepad and save your file.

Fire up Bionic Commando and enjoy being able to play it like other PC games.