1 hour 45 minutes is more than enough time for a connection at Changi, should be no problem at all.

Provided you can check in for the BA flight when you check in for your CX flight (which I think is possible on separate tickets, not sure - bags are no problem, but passengers?), you can cut it as close as 20 minutes between the flights. The OW gates at Changi are all pretty close to each other.

It would take something major to cause your flight to be almost 90 minutes late, so you should be good.