It's possible that your current wheelset could prove to be dependable, but I wouldn't bet on it. I'm not familiar with that particular hubset or those rims. Alex and Shimano both make some nice parts and some really cheap parts. Given that the donor bike was a 9-speed in 2002, they're probably decent. The real question is whether they were hand built or machine built, and I'd guess machine built. If they have nice, even tension and the rim is true, then they'd probably do OK.

If I wanted to be completely confident in my wheels for all conditions, I'd probably get something built. What I'd recommend depends on your budget.