Sigh. Wow. Was that so necessary? Maybe I should explain something to you that YOU are not understanding: people fake marriage documents in courts and churches, and do things under the table. Especially in countries like India. If that seems improbable to you, I suggest you may need a tiny reality check. Having been on this site for years and heard stories that are so mind bogglingly shocking and stupid, I never just make assumptions anymore because it turns out there is a severe amount of dumabassery and illegal crap going down daily. Don't mistake me for an idiot, and kindly don't make the mistake of speaking to me in such a manner again, please.
Anyways, you should NOT apply for him. Asking you not to put his previous marriage down tells me he is hiding something and trying to get over to the US based on a lie. If he felt everything was on the up and up he would just disclose the truth fully and let the chips fall. You are on the hook for everything he says on that application, and if they find out something isn't legitimate and you knew about it, you could be guilty of committing immigration fraud. That is bad news. You need to tell him that the only way you would consider applying for him is if he is 100% honest about everything on his application, or else he is putting your life in jeopardy. Then your choice will be to move to India and live there with him for the rest of your lives, or leave him. Never, ever screw with immigration.
As my husband's sponsor I was on the hook for his monetary needs until he became a citizen, which took five years. That meant if he ever went on welfare or was collecting unemployment benefits, I WAS THE ONE required to pay the government back, because he wasn't entitled to those benefits as a sponsored permanent resident. These are all things you need to be aware of. Eyes wide open.