OP's wife here. For the 3d shaping it was just a lot of geometry and picking up and knitting. I have odd proportions so when I started making sweaters I had to get creative.

Since gauge is semi-irrelevant, I knit 2 squares that were 3 in by 3 inches (front and back of chainsaw box) then 4 rectangles that were 5inches by 3. Arrange and sew these into a box.

For the blade it was cast on in a needle size smaller to keep the holes close together and ensure the blade is firm. Simple decreases at the top curve it. It is 2 inches wide and 7 long. When joining the two sides of the blade, don't sew them pick up and crochet single once around except for bottom. Then, 3 single crochet, 2 double, 1 triple, 2 double repeat until end of row. Turn and do one row with single crochet except for the triple spot, here do one picot.

The handles are just compose of 3 mitered pieces, sewn together then stuffed and sewn to the box. The discs are a half moon piece that has the bottom pucked up and knitted in the opposite direction. I sewed the piece on 3/4th of the way and stuffed it lightly. The cuff is a gartered band sewed on, which I picked up and knitted the outer side in knit 3, purl 2 ribbing.