If you use a single pole, double throw switch with center off position, you can wire it to get 2 leds, 3 leds, or off. It wouldn't disconnect the chip from power, just disconnect the LEDs from the drive. With a double pole, double pole, with center off, you can disconnect the power too.
Say you want to switch off the bottom LED in the string. Break the connection at its anode. Connect the switch poles to the anode and cathode of this LED, and the switch common to the cathode of the next LED up. Now, in one position the string is normal, in one position the lower LED is bypassed, and in the center position the string is broken.
This has the problem of breaking the string. I've been thinking about this. If you put an RC snubber across the switch (from common to the cathode pole), you can keep the inductive spike voltage to any arbitrary voltage across the switch. Pick a voltage well within the switch's rating, and viola! You've solved the arcing problem. Or just use a switch that can handle it and forget it. It's a pretty small inductor.
A simple way to estimate the snubber values doesn't give precise results, but I'm too lazy to calculate the exact values (which I think is pretty complicated). The estimate is close enough if you leave a little room for error. The resistor is chosen to have approximately the peak voltage across it at the peak inductor current. The capacitance is calculated by using the equations for the energy stored in an inductor or a capacitor, setting them equal, then solving for C.
R = V/I
Ec = 1/2 x C x V^2 and El = 1/2 x L x I^2
Setting Ec=El and solving for C gives
C = L x I^2/V^2