Right. If you need a low-profile LED, this typically forces you to a surface-mount (SMD) style LED.
Working with the SMD LEDs can be tedious. In addition to buying pre-wired SMD LEDs, here's another idea. The cheap LED strips of course use SMD LEDs and are available in all colors. The individual LEDs are of course pre-mounted on a flexible printed-wire strip. Nothing says you can't cut up the strip into "individual" LEDs which might make soldering wires a little easier. The photo above was from a different topic but kind of illustrates the concept. As shown in the top photo you can typically also scrape off the surface to expose the copper printed wires (traces) which is another solder attachment point.
And if your application requires a resistor, note that on LED strips, each segment-of-3 typically has 1 resistor as shown on the right side. The resistor value may not be correct for your particular application but this type of resistor goes for a couple pennies each and can be swapped.
