The short answer is you'll be fine - especially with the cheaper low-CRI (Color Rendering Index) LED bulbs.
Most white LED bulbs are made from a blue LED and yellow phosphor. The blue LED will be either 445 or 455nm center-wavelength. Warm-white (2700 to 4000K color temperature) bulbs are more likely to use 455nm, which is better. Iron-based photographic processes are sensitive to about 430nm and a tiny bit above, so not strictly just UV. Blue LEDs, especially the 445nm ones, emit a tiny bit of light below 430nm. Incandescent bulbs also emit a tiny bit of light below 430nm, and even some below 400nm (true UV).
I've read proposals to make very-high-CRI LED bulbs using UV LEDs and broad-spectrum phosphors. I haven't come across any products using this technique, however. It would be less efficient than the standard blue LED designs. So far, it looks like high CRI LED bulbs add a red-orange LED besides the blue LED and phosphors. That kind would still be fine for a darkroom.
BTW, 395nm UV LEDs are becoming more efficient and cheaper. They make great exposure light sources.
David Knierim