Control defaults to CD32 controller if cd.device is installed
From Worms Knowledge Base
The executable files used for the CD and floppy versions of Worms on the Amiga are the same. If the game can open "cd.device" (the device library, or driver, that Workbench uses to handle CD-ROM drives), it assumes that it is running on an Amiga CD32 games console and accepts input only from a CD32 joypad, not from the keyboard. This means that if you have a CD-ROM drive, Worms won't register any keyboard input,though if you have a joypad or joystick you can then go into the Options screen and manually change the controls from there.
While no official fix for this bug was made available, it can be fixed by installing WormsShell, a freeware application that offers solutions and fixes for many of the bugs present in Worms on the Amiga.
A solution to this problem was introduced in Worms: The Directors Cut - the game asks you to select your control method before it begins loading the game by pressing either the right mouse button for keyboard-and-mouse controls, or the blue button to use the CD32 controller. Updating WormsDC to 1.05 removes this option however, defaulting to keyboard + mouse set up (probably because the game refuses to load on an Amiga CD32 games console anyway).