As far as I know it shouldn't be difficult to replace the shoulder button yourself. You just need to follow the steps found here: Nintendo 3DS 2015 Motherboard Replacement until Step 9 (or until you separate the lower case from the rest of the device. As you can see the trigger buttons are not like on the DS Lites of old, but rather screwed into the casing. Remove the problem button assembly, you could try visually inspecting it to see if there is anything obvious wrong with it at first glace, put your console back together and give it a shot.
If the problem persists, you should look into getting a new button assembly, you should find those for instance on Aliexpress.