Tho a router will do; it is not meant for this kind of surface duty.
Better choice: Get the bumps out of it with planes then commit to a thickness sander.
Yes, the set of skis is the only way to go. (oops, a pivot frame will do it too!)
I would stay away from sandpaper. It will clog the pores of your workpiece and give you a cloudy finish. Instead, I would use:
1. skis or pivot frame. Do progressively smaller depths of cut until you get to within 1/32nd of your final thickness then take the rest down with a cabinet scraper. This will allow you to "fine tune" the end grain and give you a spectacular finish. Harry has some holding frames that will help nicely, too.
2. planer (as above) and then clean with cabinet scraper.
When you're using planes or a planer, make sure you oversize your workpiece just in case of tearout or other imperfections. This is not necessary with a router on skis. However, I wouldn't rely on the router bit for the finished cut. Use a cabinet scraper.
By the way, it would help if we knew where you were in the world but beyond that, we don't need your life story, detailed financial statement, description of your expensive workshop or any other personal information, in spite of what other's may say. You disclose what you wish or remain anonymous as is your want. No one here has a right to demand otherwise or restrain comment just because you chose to disclose less information than they do.
When a question is asked, please provide adequate information to allow others to comment. That is all. Missing information will surely be asked for. Photos will help too.