I would also use the table saw. And what else I would recommend you doing depends on what tools and experience you have which was why you were encouraged to fill out your profile when you became a member. If you can use a full thickness piece of the hardwood then the solution is easy. And safe. You implied that there is a gap between the tiled portion and the hardwood portion. I'm assuming that the gap is the same depth as the hardwood. What you'll do is to machine a lip on either side of a strip of that flooring. How thick depends to some extent on how wide the lip needs to be to cover the hardwood. If the lip is narrow then maybe 1/16" is enough. Wider and you'll need at least 1/4" thick. You'll set the saw fence so that with your piece on edge against the fence the saw cut will leave the thickness of the lip against the fence. The only time you'll see the blade is as it exits the cut. Flip it over to the other edge and set the fence for the thickness of the lip for the tiled side and do the same thing. Now all you have to do is set the board down flat and use the fence to get the width of the lips you need. Once again, the only time you'll see the blade is as it exits the cuts but as Stick pointed out you should be using push blocks or sticks to do this. This is an easy job and not particularly dangerous.
The transition strip won't be thick enough to touch the floor so you'll need to shim under it to support it or you risk breaking the lips off. You could take a scrap board and cut the correct thickness on the TS if you want. That might be easier and faster..
Someone I consider a master woodworker once told me that a master woodworker is not someone who never makes mistakes. He is someone who is able to cover them up so that no one can tell.