Convert ETH to BTC to save on gas fees

Hey guys,

So I have Etherum on one trading platform and I'd like to send it to another trading platform but as we all know the gas fees are high.

I wanted to ask if it would be better to take the ETH I have and buy BTC and then send that BTC from the one platform to the other (network fee lower on BTC) and then from the new platform buy ETH again with the BTC I just sent over.

Any advice would be appreciated!