I had to change mine as they were worn out. The tapered races had slight indentations making the steering notchy. This is not supposed to happen with tapered rollers, but with 10 to 15 years, and a lot of miles on streets that are mostly potholes with the occasional 10 foot long smooth area, they developed notches.
If the races are perfectly fine, they will probably match the new bearings so you might not need to change them.
On mine, after cleaning off the grease, I could see a pattern in the races. I couldn't really feel it with my finger, but I could see it. After replacing the races, the steering felt like new again.
There is no other way I can see to get them out easily. A chisel or punch would have nothing to bite onto.
The dremel required a lot of side to side switchback cuts to get across the surface. Each one has the risk of cutting through to the frame tube. I did put some scratches on the frame tube, but no serious cuts. Then you have to put a chisel into the cuts, as a wedge, to hopefully break the last few thousandths. Then there's bearing material dust everywhere, which won't do the new bearings any good, so you have to really clean everything spotlessly. It's doable, but not recommended.
A cheap wire-feed, flux-core, mig from Harbor Freight is probably all you need . They are about $90. Then a mask and gloves and little practice. Bearing races weld silky smooth and easy as long as it's clean.
EDIT: this was for removing tapered bearings which have no way of removing with a punch. The OP photos shows he has tapered races already. I assume they probably match the taper of the new bearings, if not they need to be removed. With it disassembled, I would clean the races and paint them with a Sharpie marker. Then roll the bearings in the races to see if the wear pattern on the ink is even. If only one area makes contact, then the taper may be different. I've never done this, so may be try it with the new bearings and races to see if the ink wear pattern is uniform.
Out of curiosity, if the bike already had tapered bearings, and the races look perfect, why are the bearings being replaced?
Stock ball bearing races can be removed with a punch.