Answer 1: SQUIRM
Trace SQUIRM from the left edge into the first row. Follow these cells: 1 at row 3, column 1; 2 at row 2, column 1; 3 at row 2, column 2; 4 at row 1, column 2; 5 at row 1, column 3; 6 at row 1, column 4. The letters read S → Q → U → I → R → M.
Move up, right, up, right, and right. That creates four straight segments with three turns across a span of three rows and four columns. Five of the six cells touch a board edge, while neither endpoint is a corner. Assigning this six-letter route leaves 34 open cells for the remaining four answers.