What is the risk to support server FAN replacement without shutdown system?
I am not exactly sure what you mean when you ask, "What is the risk" and "replacement"?
Are you saying you have a fan that has failed and you want to replace it
without shutting down the server?
If that is what you are asking, there are HUGE risks - depending on which fan and where it is located. You could drop a screw, or a screwdriver, or the fan. If the fan is attached to a heatsink, you could break the TIM (thermal interface material) bond. You could accidently knock loose a power or data cable. You might zap something with ESD.
IMO, as long as you are not overheating right now, the smart move is to schedule
1 hour of downtime - perhaps over this coming weekend (don't put it off too long or it will keep getting put off). Have everything ready before the downtime starts (new fan, tools, battleplan, etc.).
With proper planning, it will probably take you 5 - 10 minutes to swap out the fan. Then use the remaining time to do a proper cleaning out of any heat-trapping dust (and critters) that have settled inside. Thoroughly inspect the innards and makes sure the remaining fans spin freely and that all cables, RAM, and expansion cards are securely installed and connected. Check your cable management for tidiness. Good cable management minimizes impacting desired air flow and the risks of a wayward cable causing other issues.
If no additional problems are found, this should take 20 minutes or less.
Then put the server back in service and shine in the eyes of your bosses for completing the task in half the scheduled time!