Yes, you can replace the axle and cones and nuts, if any going with whatever thread is available, as long as you're consistent. However, the curvature of the bearing race may not be an ideal match, and more important, the dustcaps, or whatever seal system likely won't match.

Since you say it's a Shimano hub, odds greatly favor it being a 10x1 axle, which should be the most available replacement in Singapore. So, odds are you don't have to get involved in trying to match up some complete kit with cones and nuts.