Not sure it can be done easily. Like you said, the electronics would be different, and even the mounting and shaft sizes probably differ between Honda and Toyota. You can always give it a try but you'd probably find little success unfortunately.

 

I put a stitch on steering wheel cover on my '08 with the black stick-on cover trim pieces. It isn't difficult or expensive. Yours may be more torn up than that can fix.

 

Get a gently used one from a salvage parts business - lots of them online, and others here may know which ones are best. GL, and please don’t try to use the Honda part with incompatible electronics!

 

I just bought a new steering wheel for my FJ through @is_autogroup See pic. I sold the old one OEM on eBay for $100. The guy who bought it was in the business of making new sportive wheels, using old OEM wheels. You could sell your old Honda wheel and your old OEM FJ wheel, once you get it off. The FJ wheel is super easy to take off. The airbag is really on problem. Two connectors is all that's on it. A ground plug for the horn and the single connector for the steering wheel controls. If you have an Autozone auto parts store near you, you can rent a steering wheel puller. It was $50, then you get a refund once you bring it back. You have the shroud on the wheel, then just one nut on the wheel. Very easy to take off and put on. You can buy the buttons from eBay or AliExpress for $50. They come with the wiring to plug into the steering wheel. Then you'll need the axxess aswc-1 interface $68 on Crutchfield. You plug the ASWC-1 into your radio, program it, then you'll have steering wheel controls. My steering wheel was $350 which is very reasonable for custom steering wheel. All is not lost. Here is your solution. Save up your pennies.