Could you use your knowledge from other hats you've made to give you the dimensions and the do a test square to check your gauge with your chosen yarn. And just "cobble" it because you know the dimensions that you need?
DISCLAIMER: I am NOT a confident enough knitter to do this yet, but get the theory behind it.
Or I can send you a p/c of my pattern and you can adjust that?!
I'm sure you could easily adapt that for flat knitting.
I don't knit in the round at all either so I would just follow the instructions but work every other (wrong side) row in purl as I think that you knit every row in the round and it looks like stocking stitch.
Yeh what WoollybacksWife says is right - follow the same pattern but don't join it.
So cast on 35 knit 23 rows in stocking stitch row 24 (RS) follow the decreases - k3, k2tog across Row 25 (WS) purl Row 26 (RS) k2, K2tog across Row 27 (WS) purl Row 28 (RS) k2tog across. Cut wool but leave a long tail and thread it through the remaining stitches and sew up the sides.
On the instructions above I would cast on 55 or 60 stitches as the first lot of decreases are worked over 5 stitches (k3, k2tog) so you could cast on multiples of 5 and after the first decrease row you would have 44 or 48 stitches.
The second decrease row would be (k2, k2tog) and leave you with 33 or 36 stitches. (Depending on starting with 55 or 60 stitches)
The third decrease row would be (k1, k2tog) and leave you with 22 or 24 stitches.
The fourth decrease row would be (k2 tog) across the row and leave 11 or 12 stitches.
I would then p1 row and finally (k2 tog) again for the last row. This would need you to just k1 at the end if you started with 55 stitches. Either way you have 6 stitches at then end. Leave a long tail, thread through your remaining stitches using a darning needle or bodkin and use to sew up your seam.