I was wondering it if it at all possible to convert an incandescent string of Christmas lights to LEDs by simply just swapping out the individual bulbs?

If the bulbs are at least 4..5V, then technically yes. Each new bulb will then contain a pairs (one per each 4..5V rating of the original bulb, so for a 12V bulbs you use 3 pairs, for a 20V 4..5 pairs in series) of antiparallel (back-to-back, so each carry one polarity) LEDs and a series resistor, sized to yield about 1/10 of ghe original current (the voltage drop across the resistor would be about half the voltage per lamp, so for a 3-pair "12V" replacement about 6V across the resistor (be aware, you can not just sum up the voltages, because you are dealing with nonlinear components and a sinewave feed).
But then you have to replace all bulbs in the string at once. Mixing them would fry the LEDs immediately.

I'm assuming you're talking standard series-wired mini lights??

I've converted many of those sets to LED.
So yes it can be done!....but as far as what more *might* be needed (such as resistors), it depends on the type and color of LEDs you use.