I'm not sure I understand what you mean...
RuneMate uses the official Old School RuneScape client, so any third party macro/mouse recorder should work fine. Having RuneMate installed on your computer will not prevent a third party macro/mouse recorder from working.
You can then choose whether you run the macro with the official Jagex released OSRS client, or use a third party client like RuneLite.
EDIT:
Do you mean you are trying to run a bot using RuneMate, and while this bot is running, use a macro/mouse recorder to record that bot's input on the OSRS client, so you can then replay that recording without needing to run RuneMate?
If so that I strongly recommend you reconsider...a mouse recording will be very repetitive and have identical movements/click patterns. You'll be banned very quickly.