Is there a CD or LP of Cole Porter HIMSELF singing his own songs? I
heard a recording of him singing "You're the Top" and "Love Finds a
Way" on the radio 20 years ago.

Cole Porter made several recordings in which he sang his own songs.

Here you'll find a list of those recordings:

The Cole Porter Reference Guide: Recordings by Cole Porter 
http://www.geocities.com/porterguide/cole.html

This CD, a collection of great '30s songs, features Cole Porter
singing "You're the Top":

Amazon: Nipper's Greatest Hits / The 30's, Vol. 1 
http://www.amazon.com/exec/obidos/tg/detail/-/B000002WDX

A CD called "Cole Porter, a Centennial Celebration" contains Porter's
own versions of "Anything Goes," "You're the Top," and "Be Like the
Bluebird":

Amazon: Cole Porter, a Centennial Celebration
http://www.amazon.com/exec/obidos/tg/detail/-/B000002W49

The sixth CD in the "American Legends" series was devoted to Cole
Porter's songs. Most of the songs are performed by well-known singers
such as Lena Horne, Frank Sinatra, Ethel Merman, and Judy Garland, but
"Anything Goes" and "Be like the Bluebird" are sung by Porter himself:

Amazon: American Legends #6, Cole Porter
http://www.amazon.com/exec/obidos/ASIN/B000001VCP

"Cole Sings Porter" is available on CD. It was a German release, so it
may take a while to get it:

Amazon: Cole Sings Porter
http://www.amazon.com/exec/obidos/tg/detail/-/6303407684/

The German Amazon site also offers "Cole Sings Porter," and here you
can listen to many excerpts from the songs (in RealMedia format):

Amazon.de: Cole Sings Porter
http://www.amazon.de/exec/obidos/ASIN/B000001SFU

An album called "Harold Arlen and Cole Porter Singing Their Own
Compositions" is offered by "The Record Collector" website for $40 (I
presume that this is a 33rpm LP, but the term "album" could also apply
to a set of 78rpm records):

The Record Collector: Vocals A to D
http://www.the-record-collector.com/Vocals_A.htm

Ordering information for "The Record Collector" site:

The Record Collector: How Am I Supposed to Order?
http://www.the-record-collector.com/Ordering.html

Google search strategy:

Google Web Search: "cole porter sings"
://www.google.com/search?hl=en&ie=UTF-8&q=%22cole+porter+sings

Google Web Search: "cole porter singing"
://www.google.com/search?hl=en&ie=UTF-8&q=%22cole+porter+singing

Google Web Search: "sung by cole porter"
://www.google.com/search?hl=en&ie=UTF-8&q=%22sung+by+cole+porter

I hope this information is helpful. If anything is unclear, or if any
of the links do not function, please request clarification; I'll be
glad to offer further assistance before you rate my answer.

Best regards,
pinkfreud