what brand of toothpick is made of nothing but wood?

You can get wooden toothpicks from the Goldmax company. See
http://www.goldmax.com/ and click on the link for "Wooden Toothpicks,
Disperser, ..." under the Products heading at the left of the page.

Goldmax contact information:

Telephone 
(626) 964-8820 
FAX 
(626) 964-6629 
Postal address 
17747 Railroad Street, City of Industry, CA 91748 USA 
Electronic mail 
General Information: infor@goldmax.com
Sales: sales@goldmax.com
Customer Support: sales@goldmax.com 


Wooden toothpicks are also manufactured by Royal Paper Products.

See http://www.royalpaper.com/index.htm and click on links for
Woodenware & Plastics > Picks-Toothpicks - R820 for all white birch
round toothpicks,  R820  ROUND TOOTHPICK PKD 5/24/800


Both Goldmax and Royal Paper Products toothpicks are available in
smaller quantities (than wholesale orders) from www.instawares.com.



There are also many Chinese manufacturers of all-wood toothpicks - see
for example http://www.tradekey.com/ks-wooden-toothpick/

I use a local brand called Diamond. Cheap and common in Manila. All wood too.