I want to re-emphsize that I have not fragged a Goniopora before.
As Bec said:
>You could lose your coral if you try to frag it, or you could lose others to infection that sets in to that coral afterwards. <
This is always true and bears re-emphasis. IME, there is usually little danger in fragging corals that are healthy to begin with.
Below is my opinion, nothing more:
I think the important thing about fragging LPS is to make sure it's pretty well closed up first. You want to minimize the amount of damage you do to the fleshy part of the coral. Remember for some LPS, the tissue is actually well away from the area that you want to cut. If you are cutting ONLY skeleton, then you are doing essentially no damage. For Goniopora, only the branching form might have enough skeletal area free of tissue to cut in this manner. For other forms of Goniopora you are probably going to have to do some tissue damage. I don't generally use iodine dips post fragging. I don't think there would be much harm in it, I just have never really seen any need to, seems to just take more time. The theory on iodine dips (incidentally Steve Tyree advocates them) is that they surface sterlize the coral. I'm in general interested in getting the coral back into a healthy environment ASAP. Post fragging, it IS very important in my opinion to have (as mentioned above) good water flow, and a healthy tank environment (nothing stinging or pecking at the coral, good light, etc.). Always best to go back into the tank/spot from which it just came.
Regarding Dremel tools, etc. Yes, they can be nice and I use them sometimes. BUT, it really depends upon what I'm fragging. Sometimes I'll use a Dremel tool to score a coral skeleton where I want it to break, then finish the job quickly with a hammer and chisel, or a pair of cutting pliers. In this way I'm minimizing the stress on the coral because I'm not handling it too much. It's not getting hot from the Dremel cutting, or irritated from being out of the water too long. Besides, my wife hates it when coral slime gets splattered all over the room when I'm 'a Dremelin'!!
Regarding gloves. When I wear gloves it is only to minimize my exposure to coral toxins or stings. If you are sensitive to this kind of stuff (particularly toxic Zoanthids) then it's important to wear gloves. It is always of course safer to wear gloves to minimize your risk of getting tank water bacteria into a cut on your skin. That said, I rarely wear gloves when just working with corals. I ALWAYS wear gloves when I use putty epoxy as I had a very nasty allergic reaction to it once.
I usually am also not very carefully about my tools I must admit. Every year when I run my coral propagation workshop I love to see how large everyones eyes get when I take my 5 year old, nearly rusted out wire cutting pliers half covered with old electrical tape and plunge them into my tank to snip frags off.

Although I just looked for some good numbers (couldn't find any) salt water in the ocean, and our tanks is teeming with bacteria, on the order of thousands per ml of water. It's possible that the bacteria on our hands are different species, likely actually, but I don't think they are likely to be more likely to start coral infections. IMO, the important thing when fragging corals is to do as little damage as possible. With soft corals therefore it's important to have really nice sharp razor blades (clean and new), and to not crush tissue if using a scissors.
Go for it.