Cutting tool
In Episode V, Han Solo used Luke's lightsaber to cut open a tauntaun on Hoth.

Image taken from a Youtube video
Han's tauntaun had just died from the extreme cold, so Han cut it open to put the injured Luke inside for warmth.
The canon Star Wars Rebels episode "The Wynkahthu Job" (S03E07) includes an instance in which Ezra Bridger cut through a door with his lightsaber (H/T @NKCampbell):

Image taken from a Youtube video
This is similar to Qui-Gon's use of his lightsaber to cut through a blast door in Episode I, but this is a non-combat situation.
Light source
Lightsabers have been used as light sources, both in canon and Legends. Another answer on this site mentions that they were used as light sources in the canon Star Wars: The Clone Wars episode "Legacy of Terror" (S02E07):

The Jedi were with clone troopers in this situation, but were not in combat at the time.
Another answer quotes the canon novel Heir to the Jedi describing Luke using his lightsaber as a light source after his lamp was destroyed (though this may be considered combat):
“Stay back!” I warned Drusil as I heard the creature choke and spit up the lamp. It wasn’t working anymore—maybe it was simply in the off position rather than broken, but I wasn’t about to search in the dark for it in the bottom of a sewer with something hungry nearby. We needed to see, so I pulled my lightsaber from my belt and hoped it would give off enough ambient light to spot the creature before it attacked again. Holding it in front of me in a defensive stance, I turned it on as I heard the creature snarl and thrash in the filth. The blue plasma blade bloomed up and my eyes, dilated in the darkness, saw the thing open its mouth and bunch its powerful back legs for a spring at my throat.
The "Betrayed" trailer for the Legends game Star Wars: The Old Republic - Knights of the Eternal Throne has a non-combat example (H/T @Ivan Kolmychek):

Image taken from a Youtube video
Player characters in various video games can use their lightsaber as a light source. For example, in Star Wars Episode I: The Phantom Menace (H/T @Robotnik):

Image taken from a Youtube video
Also Star Wars: Jedi Knight: Jedi Academy:

Image taken from a Youtube video
(This image is a combat example, but only because that was the best I could find showing it as a light source. Having played this game, I can attest that the player is able to activate the lightsaber when not in combat.)