If you choose to save the messages to your hard drive or other external storage you shouldn't lose the smilies. Mine have definitely remained intact whenever I copied them.
Just use FILE > SAVE PAGE AS (or whatever similar function you have on your web browser) and save the whole page of messages offline. Then delete those messages from your PM inbox. If you have several pages, just keep repeating this until you've made more room.
I usually start saving and deleting the oldest messages first and work forwards.