No, you don't have to. A pre-stamped return envelope is supplied in the package.
You can simply drop it to a post box to return the product.

If you have lost the envelope, you can purchase one at Lawson or any post office, including airport post offices. 
Please ask for a Letter Pack Light (レターパックライト). The price is 370 JPY.

You can request assistance at your hotel receptions.
The return address is as below.

Og inc (Sakura Mobile)
Otakibashi Pacifica Bld. 9th Fl.
7-10-18, Nishishinjuku,
Shinjuku-ku, Tokyo, Japan
160-0023