Any turbo is going to have some lag on a B-series motor, especially a 1.6L. A WRX turbo however, would be an ideal turbo. They are quick spooling, not oversized, don't have an outragious lb/min rating (probably between 25-30 is my guess), so lag shouldn't be very noticable even if it was on a D16.
If the stock WRX turbo is comparable to a TD04-13G, it's going to spool fast on just about anything. Automotive wise, the 13G is the second smallest turbo Mitsu produces (only topped by the stock 2G DSM T-25 aka: T-2small). A 13G is quite a bit smaller than a stock TD05-14B for the 1G DSM, which flows right around 30lb/min. Lots of people have used 14B's on boosted Honda apps with great results.
If you want a quick spooling turbo, OEM stock is the way to go. WRX, 14B/T-25 DSM, K-03 VW, Ford, ect... This turbo sounds like it would do just fine on a stock internal, street driven Honda.