Is it allowed to bring sex toys on a flight to Singapore?

As already noted, airport security in Tokyo won't care. Your problem is going to be the laws in Singapore, specifically the Singapore Penal Code, article 292:

Sale of obscene books, etc.

292.—(1) Whoever —

(a) [...] has in his possession any obscene book, pamphlet, paper, drawing, painting, representation or figure, or any other obscene object whatsoever;

(b) imports, exports, transmits by electronic means or conveys any obscene object for any of the purposes aforesaid, [...]

shall be punished with imprisonment for a term which may extend to 3 months, or with fine, or with both.

So the rub (so to speak) is, what's "obscene"? Singapore traditionally took a pretty dim view of sex toys, but they've opened up a bit and there are actually multiple sex toy shops in the city now. The red line appears to be realism: lurid pink and purple tentacles are OK, realistic penises not so much.

My best guess is that your artificial vagina is likely OK, but I'm not sure I would like to have this debate with an eagle-eyed Customs officer. That said, Customs concentrates on cigarettes, drugs and alcohol, roughly in that order: unless you raise suspicions of smuggling one of these three, it's unlikely your bags will even be opened.

You have two issues: what will security in Tokyo do, and what will customs in Singapore do?

Security doesn't care what your stuff is for, or where you are going, they just care if it looks like something that might be dangerous, or is on top of something that might be dangerous. Having anything embarrassing in carry on is risky. They will root through your bag in front of everyone, open things and look inside them, etc. You can try to reduce this by being super careful about everything else in your bag - no liquids or gels, nothing knife-like, etc - but you can't be sure. To be sure, put the item in checked luggage or don't bring it.

Your title asks if you can bring the item to Singapore and you've tagged it customs-and-immigration. If you are selected for extra scrutiny by customs, generally you are by yourself when they search the bags. If they confiscate it, your family will probably not see what happens. A traveler I know tells me there are large signs as you enter Singapore reminding you what you can't bring and they are very specific - no guns, no piranha fish - so if sex toys are not allowed you will probably see a sign saying so. No sign, no worries.

Even if your bag contains no prohibited items, there is a chance that the security agent will suspect the presence of a prohibited item and search your bag. In addition, there is a chance that someone will see an image of any embarrassing item on the x-ray scanner screen.

Therefore, it is possible to answer this question without knowing whether any given embarrassing item is allowed: the only certain way to avoid embarrassment is to leave the embarrassing item behind.