No! The 1910 was built on the original 1900 to 1910 receivers with the short magazine box, while the GKs have the lengthened magazine box of the later, 1924+ models. As the magazines were lengthened by placing the rear wall (part of the receiver) more rearward by about 5 mm, GK triggerplates/set trigger assemblies are shorter accordingly by about 5 mm than the 1910 ones.
Additionally, you need not just replace the set trigger assembly, but the trigger lever (37 – 37/4) and triggerguard too. If you look at the pics above, you will see the one-piece triggerguard and triggerplate of the pre-war single trigger models, while the dst versions always had the set trigger housing instead, with a separate shotgun type triggerguard hooked (prewar) or screwed (postwar) into.