When decline is used as a transitive verb, it means "to refuse" or "to say no to": We are declining your loan application. - I regret that I must decline your invitation. Declining a customer would be a bad business move; declining your customer base is simply ungrammatical. Probably bad business too.
When a sentient actor (a person, a corporation, an intelligent animal) is the subject of decline in an apparently intransitive sense, there is generally an implied object; I would call this a "virtually transitive" use: I offered him a job, but he declined (the job). - We offered the chimp a banana, but she declined (the banana).
When a non-sentient noun is used as the subject of decline, it means that that thing/resource/quality is becoming less, or less powerful: The puma population has been declining for the past few years. - Hari Seldon says that the Empire is declining.
When a thing is declining, or a person's health or power is declining, we can say that that thing or person is in decline. As soon as his team started losing, he went into a decline. - This country's been in decline ever since they raised the drinking age.
When decrease is used as a transitive verb, it means "to reduce the amount of": I'll have to decrease my donut intake, or else my chair will break.
Sentient actors don't decrease intransitively; you can't say He decreased.
When a non-sentient noun is used as the subject of decrease, it means that that thing/resource/quality is becoming less: The puma population has been decreasing for the past few years. but NOT Hari Seldon says that the Empire is decreasing.
A crucial difference between decline and decrease in this last case is that decline can be used to indicate a loss of power, influence, significance, etc., whereas decrease can only be used for a reduction in quantity. Thus you can say both The population is decreasing and The population is declining, but while you can say The Empire is declining, you cannot say The Empire is decreasing, since there's still only one Empire.
Innoxious is used in medical, chemical, and certain manufacturing fields to mean that a substance is not injurious, hurtful, or damaging, especially to tissues. Do a Google search for "innoxious medical" and you get 768,000 results. Of course innoxious is the antonym of noxious and a synonym for innocuous. (Those three words appear in Dorland's Illustrated Medical Dictionary, 30th Ed. Nocuous, however, did not merit an entry.) Both Dorland's and Saunders Comprehensive Veterinary Dictionary include in their definitions of noxious the word "pernicious," which in medical dictionaries is defined as "tending to a fatal tissue." That is, something that is noxious can be very damaging to tissues, irreparably so.
So to answer your question, the most commonly used words (as you suspected) are innocuous and noxious. Innoxious has use in certain fields. Nocuous is just not used.
Best Answer
Of your four sentences, only the first is entirely acceptable as it stands. The rest are little ambiguous; they may represent acceptable elliptical constructions; but they cannot be used to represent the same meaning as the first.
I’ll strip out the specific words and use abstract X and Y for the nouns and abstract A for the positive adjective, with A-er as its comparative grade. A-ness is the quality expressed by A.
Sentence 1 states that X has more A-ness than Y has.
Rather than means instead of or and not or in preference to, and Sentence 2 may be parsed a couple of different ways. Most simply, it claims that X, and not Y, has more A-ness than something else—call it Z. Under this parsing the sentence is an elliptical form of
However, it is possible that X and Y are being compared to each other, as in Sentence 1. In that case, the sentence would be parsed as an elliptical form of
In both cases, however, it is the construction A-er than which performs the comparison; rather than heads an adverbial phrase which modifies the core statement.
The rather than construction can also be used to compare two verbal phrases instead of two nouns, and in this case the construction may be split:
In Sentence 3, to is a preposition which plays no part in a comparison. It may, however, be a component of a gradable “phrasal adjective” (that’s a term I just made up) like close to. If that phrasal adjective exists, the sentence could be parsed in two ways, as two different ellipses:
(But the phrasal adjective better to is not current in English, so as it stands your own sentence is not acceptable.)
The to might also be used with the -ed participle of a verb which performs a comparison; to then would be either the head of a prepositional phrase modifying the verb or a prepositional component of a phrasal main verb—it’s often hard to draw the line between these. In any case, the participle would be in positive form, not comparative, since the comparative sense would be expressed lexically:
In Sentence 4, above works the same way; I can’t offhand think of a phrasal adjective with above, but here’s a use with a participle:
But a comparison employing a comparative-grade adjective almost always implies the construction with than in your Sentence 1; so Sentences 3 and 4 are unacceptable with better or with any other A-er form which does not form a phrasal adjective with the preposition.