I thought of Lightning but that is still going to cost me a lot in transaction fees when opening a channel. And since this is a one time purchase, it defeats its purpose because, well, might as well just directly purchase using btc.
So...what can I do?
Well first of all, I think you have the wrong mindset. Is it really going to be the first, last and only time that you will be using Bitcoin for a transaction? Bitcoin is the future and the BTC adoption will continue growing. So if you want to make a long term decision then you should reconsider lightning. It will save you money in the future if you continue using it.
Otherwise I do not see any other option (other than perhaps sending Bitcoin between CEX accounts since crypto exchanges have a different internal system and on many exchanges it costs nothing to send Bitcoin to another account.
But trusting a third party with your money is not really the purpose of Bitcoin.