Is there any way I can change BED to enable me to select Sumatra pdf reader as the chm file reader?
Not easily. It would require a code change, a full recompile of BED, and testing.
I've used Sumatra in the past and it is a fine bit of software but coupling it to BED to launch
BcxHelp.chm while retaining BED's
F1 lookup capability would require some experimentation.
If I were you, I'd be more interested in discovering why overwriting an old version of BCXHelp.chm
inside
\Bed\Help\ is not working on your computer. Seems fishy to me ...