Take advantage of the fact that a) the newline character is at the end of the file and b) the character is 1 byte large: use the truncate
command to shrink the file by one byte:
# a file with the word "test" in it, with a newline at the end (5 characters total)
$ cat foo
test
# a hex dump of foo shows the '\n' at the end (0a)
$ xxd -p foo
746573740a
# and `stat` tells us the size of the file: 5 bytes (one for each character)
$ stat -c '%s' foo
5
# so we can use `truncate` to set the file size to 4 bytes instead
$ truncate -s 4 foo
# which will remove the newline at the end
$ xxd -p foo
74657374
$ cat foo
test$
You can also roll the sizing and math into a one line command:
truncate -s $(($(stat -c '%s' foo)-1)) foo