dd
has a skip option.
Per file You can use dd if=MyFile of=my_new_file skip=BytesToSkip
Optionally in a loop (e.g. in bash in the target directory)
for a in * ; do echo processing $a ; dd if=$a of=$a.shorter skip=300 ; done
Adjust skip with the correct number of bytes, KB or MB
If the files are large playing with the block size (bs=X) might speed things up.