Sorry I am not sure right now what "right bearing tool" you are referring to but as far as I know you would still need to get the axle out before you can take the bearing out.

So you would need to unconnect the hub anyway - at least partially. You need to at least unbolt the strut and take one of the control arms out. At that point you are only two bolts away(tie rod and second control arm) from removing it all. So I think for most people it makes a lot more sense to just remove it entirely and take it on a press.

Check and replace/service your ball joints, control arms, brakes and such at the same time - these parts are all so cheap now.

We used this kit, and more specifically the 3 legs puller on the left to push the axle.