Shouldn't be a problem (especially if you don't have arrows), it's "sporting gear".
I took bows to the US and came back with some staves and a bow no real problem all transported in a plastic drain pipe.
On the way out they asked if the arrows were "pointy" I chose to assume they meant broadheads, so I could answer no (they were field points).
On the way back I had a Native American bow made for me by a guy over there and some arrows (one stone point, one broadhead "trade point" and a field point). I would have described them as decorative items if I had been asked, but I wasn't.
I ignored the various archery sporting goods allowances as they weren't long enough and only really catered for takedowns or compounds... (wouldn't recognise a real bow if it bit them on the leg). I took it through to oversize baggage. (Didn't cost me).
Read the baggage size allowances for your flight, I had to trim about 1/2" off the nocks of one
ELB to fit inside the allowance!
Don't volunteer information, just answer any questions.
You'll need good solid backaging to avoid baggage handlers breaking it or playing with it and stringing it backwards. (Label it archery equipment or sporting goods... not bows and arrows.)
Del
PS. Don't forget to collect and re-check stuff back into oversize items on connecting flights... I got caught out, having being waved into line whilst carrying my 6' plastic pipe. When I got to security they turned me back as it was too big to carry onto the plane! One nice chap, walked me back to oversize baggage and brought me back to save queuing again.