The Conrad is a lovely hotel. I was there last night.
You'll need to walk over to Wall (probably a 10-15 min walk). It's a fairly straight walk across town (your hotel is in Battery Park, lower west side of city and Wall is lower center), or you could hop on the downtown 2 or 3 train (nearest subway is Chambers) to Wall. The Wall St store is across the street from the NYSE.
To head up to Madison, you can take the 4,5 (green line) to 59th street and then walk 2 avenues over and 3 streets up to Hermes Madison. Other subway you can take is the R train (yellow line) to 59th/5th stop, and walk 1 avenue and 3 streets up. Both of these subway lines are right by H Wall St.
Generally speaking, the green line runs more frequently than the yellow line. Also, the 4 and 5 trains run express (R is local), so it will be faster. I'd say, it should take you 15-20 mins to get there, if that; 5 stops on the train. I worked on Wall St for a very long time and used to make quick trips uptown and was typically back in my office in under an hour.
If you are heading directly from your hotel to H Madison, that will take a while. I can give those instructions if you like, but 40-45 mins sounds about right.