The easiest way is with a rework station(some refer to it simply as hot air gun, but a hot air gun may be too big for this kind of work), you can heat all pins at once with it.
If you don't have one, what I would do is add solder to each side of the chip until all 4 pins on that side are connected by the same bib blob of solder. This way, you only have two places to heat up, and since this does not look like a board made to dissipate heat, you can heat one side, then switch to the other and heat it up while the other is still liquid. So basically get some tweezers, and keep pulling the chip, heat one side until it liquefies completely and quickly switch to the other side, you should be able to heat enough before the other side cools and the chip should come off. You can then remove the excess solder with the chip outside by various means.
Remember to not take too much time making the blob or heating up, as it could harm the component. I could not find a picture of what I mean with blob of solder, but I thinkyou get the idea, just add solder until the 4 pins are connected.
edit: I see you mentioned soldering as well, I do think it is easier:
Remove any excess solder from the chip and the board. For this kind of very spaced pins, a solder pump should suffice. If you don't have one, you can use wick, if you don't have wick, try a copper wire with flux next to it, the solder should cling to the hot copper wire.
After cleaning, position the chip in the desire position using tweezers, and solder one of the pins. Then solder the most distant pin from the one you just soldered. This will keep the chip in place, so now just solder one pin at a time. Use flux in every part of the soldering process.