Is it normal for DC wall adapter power supplies to provide voltages above the nominal ones?
Yes, this can be normal.  There are two kinds of wall-warts -- regulated and unregulated (the latter are usually cheaper).

You have two of the unregulated ones.  These provide their rated voltage (e.g. 9v) under the load specified on their label, but the no-load voltage can be much higher as you have discovered.  It probably won't hurt to use the one outputting 15v, since under the load of the board it will be closer to its rated voltage.  But frankly, I wouldn't chance it.  Use the other one instead.