Bet on rising rates while minimizing negative carry?

Hi all,

I am a junior equity analyst at a bottoms-up shop and have limited knowledge of derivatives. I am trying to figure out how one would go about betting that interest rates will rise more quickly than the market expects over a long time horizon. If you short bonds, you're paying the yield and borrow cost, and if you short the futures then there's also negative carry because the futures have to be in backwardation in order to avoid arbitrage opportunities for someone who buys the basis for the yield and locks in the trade with the future.

I am thinking that interest rate swaps can potentially avoid the negative carry. The thought is that, unlike with the bond and futures trades where the short yield guy has a counterparty who is long yield, in the swap case you are also short yield because you are paying the fixed, but the counterparty is someone who is also short yield (namely, they are paying the floating). And since the fixed and floating have to NPV to zero, there shouldn't be a carry cost to this trade, strictly speaking, so long as you hold the trade to maturity and the actual LIBOR that we get in the future follows the trajectory implied by the swap curve when you enter the trade. What am I missing?

Apologies if this is an extremely basic question. I poked around this forum for an answer to this but couldn't really find one.