Order does not matter. Only exception is FPGA, you need to upload ADR file, unmount and mount DFU, then upload FPGA’ BIN, unmount, and finally restart your DSO if you finished updating. Note that restarting the DSO is not necessary if you did not finished updating.
By the way, it is impossible to kill DS203 by updating it, so no need to worry. However, it is better to write down your license number just in case you ever need it, read seeedstudio.com/forum/viewtopic.php?p=9337#p9337 if you do not know how to get your license number.