If you want to try a different SMS app, try GO SMS Pro. It's free and has this functionality built in.
However, it's going to be nearly impossible to find one with few permissions. Think how many permissions it would need because of what it does:
-Access to contacts
-SMS/MMS
-Services that may cost you money
-Find accounts (google)
-Write SD card storage
By default, it needs many. Just be sure to read what they are and if they don't make sense, don't install. Most of the time, you can figure out what they're for.