Yes. I have walked up to Schiltorn from Lauterbrunnen (2200m up) three times.
 
When are you going? I did this hike last August/September, but even that late in the season there was a fair bit of snow for the last 50 meters or so. The last 100-200 meters up to the Schiltorn can be a bit of a scramble, some of it quite exposed.
 
From Lauterbrunnen it took me 4.5 hours to get right to the top, but this was at the end of a hiking holiday and I was uber-fit by then  From Murren (about 45 minutes from Gimmelwald), its about a 2.5 hour walk. Its not a technical hike, but the walk up from Murren to Birg is the post brutal, calf-destroying hike I’ve ever done. Its relentless! The views are stunning tho and the food in the Schiltorn is excellent.
 
The last few hundred meters to the Schiltorn involve a bit of a scramble which is probably iffy if its snowed in. But you can easily walk as far up as Birg (another cable car station just before the top) and get the cable car up to Schiltorn for the last few hundred meters.
 
Its doable but relentlessly strenuous. You’re not in over your head, but consider taking the cable car from Birg to Schiltorn if its still snowed in up top.