Do toy story toys require a disney purchase for exclusivity?

Toy Story is a 1995 film produced by Pixar Animation Studios and directed by John Lasseter. The narrative and production details supplied do not mention any exclusivity arrangements with Disney regarding the toys based on the film. While Disney did approach Pixar to produce the film, no information in the sources states that Disney owns exclusive rights to sell or distribute Toy Story merchandise. Therefore, based on the evidence at hand, there is no indication that purchasing a Disney product is necessary to obtain authentic Toy Story toys.