There's several options:
1. The .400" wide triggers also came in a smooth version. If you search for those you'll save time and/or money getting the grooves out. And you'll have the case colored finish on the face of the trigger.
2. Much easier to find and a cheaper alternative is to use the smooth combat trigger that became standard on all models in the early 1980s when all the target trigger options were discontinued. They're wider at .320" wide than the old standard .265" wide trigger. The K, L, and N frame triggers are all the same and interchangeable.
3. Not removing the grooves completely, just to 1/3 or 1/2 the depth is usually satisfactory for preventing a sore trigger finger and the factory appearance still remains.
4. That's a great video above and similar to the method I use. It's a task made for the use of a Dremel tool. But only for the person with a little skill and practice at using it! The most common error to guard against is letting the tool slip off the trigger face and gouging the sides of the trigger; especially with the skinny abrasive wheels!
Once that happens, it's a lot of extra work to get out the gouges, plus the case colors on the sides of the trigger are lost.
Using the abrasive wheel at an angle as shown in the video for the final polish is very risky business. It's extremely easy to slip on to the edge as mentioned above, and also wind up with low points and gouges that take extra final sanding to remove.
5. I always finish up by sanding the surface with 320 grit paper wrapped around a 1/2" or 5/8" wood dowel to completely level the surface, and finally with 400 or 600 grit (your choice) for the final surface finish.
6. Touching up the face of the trigger with cold blue after putting oil on the trigger face surface will give a mottled coloring that resembles the factory case colors. The rougher the final finish like with 320 or 400 grit, the better the touch up finish will last. A final high polished surface will wear away the fastest.
7. If I don't need to take apart the action for a deep cleaning, I remove the grooves with the trigger still installed. Cock the hammer and use a large pencil eraser to prop the hammer back for when you press the trigger too hard and trip the hammer. This will provide access to the grooves on the entire front face of the trigger. Heavily tape around the entire inside of the trigger guard for protection from slips with the tool and sanding paper, and to seal out grinding grit around the trigger opening.
I hope you find these options helpful,