Should be the same process as for a complete fluid flush, which is about replacing all the fluid.
- Crack open the bottom bleed port to let the old mineral oil out.
- Fit some suitable clear hose on and run it to a bottle or bowl to catch the oil.
- Pump the lever until the brake stops dropping oil. You may need to open the top fill screw to let air into the system.
- Let the bike stand for a while - You're trying to get the last traces of oil down and out. This should be easier on a hot day.
- Then fit a fill cup and start filling with new fork oil. Hopefully the new fluid is a different colour and you can see when it starts coming out the bleed hose at the bottom. Otherwise you'll just have to bleed it till the air bubbles stop, and then a bit further for confidence.
But you're electing to replace the Mineral oil with something calling itself "fork oil" which is already out of spec. Its your choice if you want to replace all the brake hose and detail-clean both the caliper and lever to avoid the old fluid contaminating the new.
I cannot find details of whether this fork oil is mineral-oil based or if it is something else and may attack your hose and seals, in the same way using brake fluid would.
If you're committed to this idea, consider just doing one brake and leave the other with the stock fluid, for comparison purposes. Personally, I'd use the right fluid - brakes are too important.