Repair shop suggests to solder new graphics chip onto a used graphics card
Speaking from experiences in the repair community: Its unlikely that its actually a new unused chip. A lot of sellers try to find working chips and clean them and brand them as new. (Some even going as far as lasering in a new date code to make them look like they came from a recent batch, even though the chip has not been produced for a while).

Even if the graphics chip would be new it has the same design faults in there that made it die in the first place. That combined with being unsure about the practices, heat settings and how the chip was stored makes it very uncertain for how long it will last. 

My advice: If the store is willing to do this for less then $80 you might want to give it a try (while also saving up for a new device), higher then that and I personally wouldn't risk it.

To answer your second question, there aren't many safety concerns. If a graphics chip shorts out the system will just disable power. I would say the electrical risk is close to none and not more then it has always been