I think the HSUS (Humane Society of the United States) has a very well thought out position on this issue and one that is worth considering....

The HSUS condones transfer of euthanized animals from shelters to research or educational institutions under only very limited circumstances. First, no transactions of live animals should occur, and any animal involved must have been humanely euthanized due to either mortal illness or injury, or because no suitable home could be found for the animal within a reasonable time.

Second, animal cadavers may be transferred only when the animal's former owner has been informed of this policy and has given consent. Full public awareness of any animal transfer policy is vital to maintaining public trust in animal shelters. Regardless of owner consent, however, shelters not wishing to supply animal carcasses to institutions should not be compelled to do so.

Third, such transfers should not involve elementary, middle or high schools. The HSUS opposes the practice of animal dissection in pre-college classrooms for numerous reasons. At the college level, we acknowledge the need for animal cadavers in veterinary training, for instance, but emphasize the importance that any cadavers come only from humanely euthanized animals and that no animal be raised or killed specifically for use in dissection.

Fourth, transfer of animals from animal shelters must never involve any exchange of money. The existence of so-called "surplus" cats is a result of the tragedy of pet overpopulation. Millions of cats are killed yearly in US shelters because there are not enough homes for them all. When there is money to be made in dealing in their carcasses, there may be less incentive for addressing overpopulation. There is also the perception that the shelter would rather gain from this tragedy than spend their monetary resources necessary to solve it.

Finally, when the above criteria are met, it should be explained to students that the animals are from an ethically sound source.
http://www.hsus.org/ace/11373?pg=2

Personally, I feel that because you really have no way to insure that these cats were obtained from an ethically sound source you have to assume that they were not obtained ethically. According to your post it looks like you only felt dissecting a cat might be okay if it wasn’t killed "just for" your dissection. However, if a little money transfer were involved from the humane society to the laboratory then it is easy to see how to some uncaring individual a cat would be "worth more" dead than alive.

My vote would be to object to this dissection.

If you come to this same conclusion then I suggest you look to this helpful guide put out by the National Anti-Vivisection Society for advice on how to proceed: http://www.navs.org/education/pdf/HSbooklet.pdf

They even have a toll free numbers you can call!
If you need specific suggestions for alternative course work, see the Alternatives Loan Program listing or call NAVS at 1-800-888-NAVS (6287).
If after reading this booklet you have more questions about how to proceed, feel free to call us at our toll-free number, 1-800-922-FROG (3764).