Laptop battery pack rebuild; what cell discharge rate?
Ask yourself this, can I remove the battery from the laptop and still have it run fine if it is plugged in? I am assuming this is a yes. This would mean that the load is being met by the supply from your battery charger. So, so long as you have the same continuous current capacity from your battery pack that you do from your charger you should be set. 

If we assume that that rate is less than 5amps, (you have a pig of a laptop if it is that much) then you are golden as almost all genuine 18650 cells can source at least that much. Many source up to 15-30amps even. 

You are also asking if it is safe to have too high of a discharge capability of your cells: No, not really. If you draw only 5amps out of a cell that can source 30, that is fine. The cells will always run a cooler than if you were taxing it more. So that is good. 

If you want a bit more help, I would recommend the sanyo ncr 18650 ga cell. It can source up to 10amps continuously. You only need &lt;5amps so it will run nice and cool. It also has one of the highest capacities of all the 18650 cells available these days so your battery will last nice and long between charges.