At which point the capacitors will have leaked to the point of causing significantly more damage to the board than if you'd just replaced them outright.
With all due respect sir, this is terrible advice. 
Besides... it's an A1200. It's a circuit board in a plastic case. Hardly "rocket science" type of innards. 
If the system is running fine and the caps haven't leaked or the tops popped up, then it's absurd to have someone open the system and have the board re-worked, unless you have more time and money than common sense. And board replacement is probably cheaper than having the caps replaced anyway, not to mention the down time waiting for someone with the solder skills to do the job. A replacement board from AmigaKit is only $64USD. If you can find someone who will recap an entire board for less, then be my guest, but you better also ask them to guarantee their work hope they don't fudge up anything else on your existing board.