Well, for starters, I don't think the novels ever make it very clear why the male hybrid's saliva contains venom and the females don't; it may be gender linked, it may be random genetics. But that's not terribly relevant, as we can still group the hybrids into two categories: those that don't produce venom, and those that do, and still ask:
If a vampire hybrid that is not venomous is bitten by a vampire, what happens?
The only canonical answer is "no one knows", because it's never happened in the novels, and presumably won't happen on-screen. There is talk of continuing Twilight well past the end of Breaking Dawn - Part Two, possibly as a television series; depending on who they get to write and direct that, we may or may not get some internally-consistent mythology to draw from, and can maybe answer this question.
For now, they best we can do is make an educated guess, based on what we do know about hybrids and vampire venom, and extrapolate that into real-world biological processes.
When injected into a human, the venom attacks their cells and slowly (and painfully) converts them into a vampire. When injected into a vampire, the venom causes some temporary, mild pain. The key questions we need to answer, then, are "What is it about human cells that the vampire venom attacks?", and "Do hybrid vampire's cells have that?"
The action of vampire venom appears similar to snake or insect venom, so lets assume it works the same way as well. Venom attacks the proteins that make up human tissue. Typically, it will attack structures on the cell walls that cause key biological processes to fail, or even the cell walls to rupture. This is very similar to how antibiotics attack bacteria, for example. And just like antibiotics bind better, and thus have more effect against some bacteria than others, vampire venom has more of an effect against human cells than vampire ones. Therefore, it seems logical to assume there is some molecular component expressed on the cell walls of vampire tissue that is distinct from human tissue. (This idea will be reinforced in a bit -- the receptors on the cell wall are a product of the DNA sequence.)
So, the venom most likely attacks something that is found on human cell walls, and not vampire. Would a hybrid have this "venom targeting factor"? Probably not.
(Quick side-note about the genetics. The Twilight wiki claims that hybrids have 24 chromosome pairs; I don't remember that detail but, if true, would almost certainly reflect a genetic defect in the hybrid. There's no way for a hybrid to get an extra pair of chromosomes naturally from a human mother; at worst it would have two extra unpaired chromosomes from the father, and then only if vampires had 25 pairs. If you introduce the idea of genetic defects into the mix, the rest of this hypothesis sort-of goes out the window, so I'm going to ignore it for now.)
A hybrid does not have "human cells" and "vampire cells" -- that's not how genetic hybrids work. The cell has a mixture of genetic material, 50% from each parent, in a combination that just happens to be viable. In order for this to work, the genetics of the two parents must be similar enough that their combined DNA can still code for valid proteins that perform the tasks needed for "life". Presumably, as former humans, vampire DNA is extremely similar to human DNA, so that's good. But hybrids inherit enhanced attributes -- speed, strength, etc. -- that come with being vampires, so those must also be coded within the DNA, meaning vampire DNA must be slightly different from humans. That fits well with the idea that vampire cells are structurally close but not identical to human cells.
Given all of that, I suspect the answer is that lots of pain would happen to a hybrid that got bitten, but probably not anything permanent. Their cell walls would not match exactly what human would be, but would be about halfway (on average) between the vampire and human cells. Thus, the venom would likely find some receptors to bind to and cause cellular disruption, as it does with vampires, only more efficiently. But it likely would not be able to fully bind to the cells and perform whatever transformation process it would against a human cell.