LED's are current devices, not voltage devices. A slight increase or decrease will not do any significant harm.
Well... not exactly. Without knowing exactly how the accessory is wired, that assumption is somewhat dangerous. A little voltage changes current a lot with an LED if you have no current limiting. For common 3V blue or white LED's the voltage/current knee is quite sharp. Take a common 20ma rated LED for instance. At 3.3V the white LED is drawing about 16ma, but at 3.4V the white LED current is already way over specification at around 35ma, and at 3.5V it's at around 45ma. So, in .2 volts we went from well within the current rating to over twice the current rating. Most folks would consider a .2V change as a pretty slight increase.
Of course, a decrease in voltage is unlikely to harm the LED, running below their rated current is fine.
Alan, I suggest you follow the suggestion of adding a diode, that will insure you don't do any damage.