Really, just try a few things before the last resort. The foam filter as can be seen in your first photo will just pull out of the metal cup it sits in. Just give her a good cleaning, make sure its dried out, and see if you see an improvement. The fuel filter just pushes onto the end of the fuel line inside the gas tank. I usually use a bent metal wire (coat hanger before they turned plastic) to fish them out. A new filter is only a few dollars.
If these fail, I can understand you being intimidated trying to put in a carb kit. I can't tell you how much a shop would charge to diagnose the saw, but I'd imagine it'll be at least $20 to $30. Best thing to do is ask local shops and see what they say. If you decide you want to try to do a carb rebuild, its really not that difficult. I'm sure you can get plenty of help here if you deicde to take this approach.
Dan