I had this same problem with a DR Trimmer that was inadequately stored. I put some Sea Foam in the gas and ran it for awhile. Cleared the problem up. Certainly give it a try before trying to disassemble.
By the way, I have the same Honda. I put Stabil in the gas, then I run it to warm, shut it off. Take off the access cover. There is a "brass" screw that is in the carb line. Back this screw out a bit and it will drain the carb bowl and gas line. Then turn the screw back in to seat it. This way you don't have to run it at all when stored. I always put mine away this way. It sits for months sometimes without running. When I need it, I just turn on the switch and pull until it starts. It always runs perfectly.
2012 F150 FX4 Ecoboost, 2016 Surveyor 274BHS
2003 Yamaha FJR1300, Demco Premiere Slider
1969 John Deere 1020, 1940 Ford 9N, 1948 Ford 8N
Jonsered 535, Can of WD-40, Duct Tape
Red Green coffee mugs