Do you need to remove or soften exoskeleton before embedding and sectioning invertebrate samples, or will the tissue still cut well with the exoskeleton present?
I worked most on insect tissues, but I can provide you with some hints.
I don't know which method of sectioning you want to use, or the dimensions of the pieces involved. If you want to use a freezing microtome, I don't think it will work - if you want to perform some histochemical studies, I suggest you to remove any hard part (e.g. exoscheleton) from the piece you want to work with. The removal of the exoscheleton aapplies also to the paraffin embedding method. Some tips:
1) Use a decalcifying fixative (e.g. Duboscq-Brasil, or some trichloroacetic-based one, which will remove most of the calcium carbonate present in the exoscheleton);
2) A post-fixation in an aqueous Ethylenediaminetetraacetic acid (a.k.a. EDTA) solution (which binds calcium, and by this softens the tissue), or;
3) Fix in 10% formalin, after that use formic acid 22 to 35% or a mixture 1:1 of formic acid and formalin,
4) Or fix in formalin as previously and after that use: 10% trichloroacetic acid;
5) An aqueous solution of up to 30% sodium hexametaphosphate,
The tissue is decalcified enough when it' can be easily penetrated by a needle or scratched by nail.
(from: "Precis de microscopie, 2eme edition" by Langeron - it may be useful).
Last but not least, the decalcified objects become very hard when included in paraffin. You can use a celloidin-based embedding (which hardens less the tissue), but I think that the removal of the exoscheleton remains the best option.
I and my colleagues have been working on American lobster and other calcified Decapods. You ask about cryosectioning which suggests you want to do histochemistry. The answers previous have dealt with that issue suggesting various methods of decalcifying and I agree with those suggestions. We are interested in the calcium carbonate and carbonate apatite components of the cuticle and potential storage in underlying tissue. In that instance two methods of seeing the surface are used which are not 'thin sections' per se but allow viewing at high resolution. After fixation by freeze substitution the tissue embedded in plastic or as a tissue block can be polished using a diamond knife or mineral polishing methods. The diamond polishing allows such surfaces to be analyzed by various analytic techniches such as microRaman Spectroscopy, Atomic Force Microscopy, Electron Microprobe and other surface scanning techniques. Unfortunately the creation of thin sections is not a reasonable approach without demineralizing because the shattering of the minerals and damage to the diamond or glass knives used is too extensive to allow more than perhaps one section to be obtained before the sectioning becomes meaningless. We have found that focusing on using methods that observe the chemistry on polished surfaces is a more productive approach. These are methods that need to be developed in some cases for observing the tissues in intimate contact with the cuticles and shells involved.