There might be many different options for you to upgrade or replace your processor with. We recommend contacting the computer manufacturer as they have set the valid compatibility list between the computer, the BIOS and the available processors in the market. The system manufacturer should also provide the specifications on what technologies from the processor might or might not be supported.
Please bear in mind that what limits the compatibility is the computer itself (motherboard and bios) not the processor. The motherboard requires to have the proper micro code to manage the processor, if not, the system will not work, and it is the computer manufacturer or Original Equipment Manufacturer who develops the BIOS to include the micro-code for the processor. That is the reason why, the processor that you currently have on your system is able to work properly even while not being not listed as compatible on the web site you mentioned. So, for compatibility information you need to check with your laptop manufacturer.