I am trying to find a retail or wholesale company for manufacturing,
packaging and marketing a simple USB PC peripheral, WITHOUT A
PATENT-Patent Pending, preferably in the US.

Greetings -

I know of a single "multi-hat" company that does just what you're
looking for, and I believe they will take on your project without a
patent-pending.  However, I strongly recommend at least getting what's
called a "provisional patent" on your device, which is basically a
comparatively inexpensive patent "placeholder" that enables you to
file a patent within a year.  This will offer you at least a little
protection.  See www.uspto.gov for more info.
 
The company is called T. Pico International Inc, of Utah.  See
http://www.tpicointernational.com/Manufacturing/manufacturing.html 
and http://www.tpicointernational.com/Distribution/distribution.html
for more information. Their phone number is 801-886-0377.   If they
see enough value in your product, they will financially back it
themselves.
 
Your question asked for one particular company to suit your needs. 
Please ask for additional clarification, if needed, before rating this
answer.
  
Thank you,
  
jbf777-ga

Good Answer. I like it, I have sent a e-mail to the company via the
web page provided below awaiting there response. It would have been
nicer to have a second or third company in the USA or Asian to have a
choice. However, I am grateful for the Answer; this would have taken
me ages.

Thank You :-)