Is This Statement/Sentence Correct, Grammatically?

Yes, the sentence, although awkward, is grammatically correct, and non-contract and custom-order are correctly hyphenated. Noncontract and customorder are not words themselves (run it through the spelling check), and the hyphen is required to make them into "words," in the sense of having a discrete meaning which only arises from the combination.

I'd add a comma:

"non-contract, custom-order aquariums"

Exactly what does "non-contract" mean? My assumption is that the aquarium builder doesn't require paperwork, but this wouldn't make sense for a profitable made-to-order business.

Legally it doesn't entirely make sense either. A contract only requires an "offer", "acceptance" and exchange of something of value. Contracts don't have to be written, though they are highly desirable to fix the actual conditions of the agreement. Time, materials, cost, method/time of payment, and the certain identities of the parties are the sorts of disagreements that can arise over what was contracted for. Those details, if not written down can cause endless grief later. Without a written agreement that all the parties signify agreement to, it's hard for a court to determine whether or not an agreement has been violated. Oh well, that wasn't the question posed.

Both the sentence and meaning would be improved by just editing out "non-contract". We have enough trouble communicating even simple ideas, and to make that task more difficult by cluttering up our sentences makes little sense. However, the sentence is grammatically proper.

I would also use a comma between contract and custom.

Re: Is This Statement/Sentence Correct, Grammatically?

I'd spell "equipment" correctly. Otherwise it's fine.

Non is a prefix. According to American rules of spelling, it should be connected to the word without a hyphen: noncontract.