I'm wondering if it's worth exchanging Bitcoin to Monero for security as Bitcoin is quite volatile and monero seems less so. Any advice would be appreciated.
What's your goal generally? Taking care of the profits and minimizing the risks of losing?
That will not work and Im sure of that. No doubt that all altcoins are dependant on bitcoin price so even there is no price movement on Monero still it's not excluded once bitcoin price makes a surprising move again whether uptrend or downtrend.
Since we are all just making statement here, you will never know until you try. You can test it on actual and see what it will gives you. Yes give it a try and "risks" some then come back after a period of time.