* `| wc -l` prints the number of lines.
* `| wc -c` prints the number of chars, including newline.
* `| wc -lc` prints both (number of lines first).
So you can simply subtract them: (write it instead of `|wc -c`)
| wc -lc | awk '{print $2 - $1}'
If you only print your sequence on one line, you can substract 1 instead of the number of newlines.
Or you can use `awk` only, match the whole line and count its chars:
| awk '{match("[A-Z]*");print RLENGTH}'
`RLENGTH` is the length of the match (here, it's the whole line). Here, I assume you use only capital letters, else, use `.` instead of `[A-Z]`.
On `vim` (text editor, so it could be incompatible with your script), visually select your area (one line or more) and run:
:'<,'>s/[A-Z]*//gn
You can also delete the newline characters with `tr` (also works for several lines) :
| tr -d '\
' | wc -c
Btw, there is probably lots of other ways to do it.