It's my guess that yes, you would want a softer shock spring.
I also highly recommend you get the shock, itself, revalved at the same time if you have the money.
Worth it if you are looking for the best you can reasonably make the bike.
Edit:
In fact, you would be well off to pay attention to the front end, as well.
Often, changing one end will effect the other, or the bike will feel/work better when both ends are scrutinized.
Example of this is when I had a softer spring installed on my WR-250X, the front end - not surprisingly - then felt that it was riding too high compared to the rear.
I used the stock springs, but lowered the oil level a bit (approx 10 mm) which effectively reduces the spring rate a bit by softening the "air spring" effect of the forks.
This minor change was enough to restore a balanced front-to-rear feel.
If you contact a suspension shop, look into both ends.