Having budgeted a trip around the world in a 182, we came up with required funds of around 100,000 GBP.
Flying around the world is not a good means of raising money for charity unless you can self-fund the actual costs, and raise money on top of that.
In that case, common aircraft for this kind of trip are Cirrus SR22, Piper Comanches, and Bonanzas.
The only Diesel that are really available are the Austro/Thielert of the Diamonds, and a few SMA generation 1 engines flying in 182s.
I have about 140 hours through Africa in an SMA 182 and I'd be wary of using it on a round-the-world; the alternator fails with worrying regularity, mostly through fatigue failure of the connections from the high vibrations it seems.
The Thielert engines (I've only around 20 hours behind one of them) are known for poor reliability and I wouldn't fly one over long stretches of water. I did the Med a couple of times in one from Sardinia to Tunisia and that was more than enough. The Austro engines have a better reputation; however, unlike the SMA engine (which has a mechanical back-up mode), they will fail if electrical power is lost.
An Austro engine with a mechanical back-up mode would be good for round the world but doesn't exist. In lieu of that you could consider a DA42; two engines, and added electrical redundancy. As long as you have a system to dump the extra ferry fuel in case of an engine failure you'd probably be in decent shape with one of them.