There are two versions of Shrimp Butter in the classical French canon.
Cold version (à froid):
1 part cooked shrimp puréed with an equal amount of butter, then pressed through a sieve.
Use for cold hors d’oeuvres, cold fish and fish sauces.
Hot version (à chaud):
1 part cooked shrimp puréed, blended with an equal amount of butter, then melted in a bain marie, strained through a cloth into a bowl filled with iced water. The melted, strained butter will congeal: collect it out of the water and put in on a cloth to dry. Use in sauces, soups and seafood stews.
In both versions, for the shrimp you may use either shrimp flesh, or just the shells of the shrimp. All that you are after is the flavour.