MySQL provides a level of statistics for your INSERT, UPDATE, DELETE, REPLACE Data Manipulation Language (DML) commands using the STATUS output of various Com_ variables, however it is per server stats. I would like per table stats.

You can achieve this with tools such as MySQL Proxy and mk-query-digest, however there is actually a very simple solution that requires no additional tools.
The following 1 line Linux command (reformatted for ease of reading) gave me exactly what I wanted, and it had ZERO impact on the database.

$ mysqlbinlog /path/to/mysql-bin.000999 |  
   grep -i -e "^update" -e "^insert" -e "^delete" -e "^replace" -e "^alter"  | 
   cut -c1-100 | tr '[A-Z]' '[a-z]' |  
   sed -e "s/t/ /g;s/`//g;s/(.*$//;s/ set .*$//;s/ as .*$//" | sed -e "s/ where .*$//" |  
   sort | uniq -c | sort -nr


  33389 update e_acc
  17680 insert into r_b
  17680 insert into e_rec
  14332 insert into rcv_c
  13543 update e_rec
  10805 update loc
   3339 insert into r_att
   2781 insert into o_att
...

Granted the syntax could do with some regex improvements, but in 2 minutes I was able to deduce some approximate load. The mysqlbinlog command also gives option to retrieve data for a given time period, so it is very easy to get these statistics on a per hour basis.

Sometimes the most simple options are right in front of you, just just need to strive to find the simplest solution.