Hi Sharkbait,
Your African safari sounds like a super exciting and fun trip. It will most likely be experience of a lifetime.
We just returned from a trip to India and spent a few days in a safari in one of the national parks there with the hope of getting to see a Bengal tiger in the wild.
My extensive research in choosing binoculars clearly pointed to 10X magnification for safaris, especially in Africa. You will be seeing wildlife in most cases from far (and safer) distances from your vehicle in an open savanna topography, so you will appreciate the extra oomph that a 10X binocular will offer - especially if your eyesight is subpar, as you describe. 10X is also good for birding if one lives near the coast, lakes or estuaries which also happens to be my case. 8X would be a better choice for forest, mountains and places with denser vegetation. Having said that, I am not familiar with the topography of Singapore to give you a proper recommendation for birding purposes. But, personally, I feel 10X has not hindered a bit my enjoyment of birdwatching - quite the opposite.
As far as brands go, the recommendations other members have given you look solid at the $/€500 range. Hope you find a pair that works well with your eyeglasses.
PS. And, yes, we did see Bengal tigers in our Indian safari, a mother with three cubs. Sorry these are not great images as I was handholding both the iPhone and binoculars. But I am happy the moment was captured as these tigers were barely visible to the naked eye at that moment.
The momma later hunting for food and MUCH closer to our vehicle (iPhone shot only). I think we were all in state of ecstasy.