That's probably going to be problematic. How would the online service connect to your
local database to perform the queries there?
SQL Developer doesn't install itself, you just unpack it and run it. True, it takes ages to start, but it should not slow down your laptop when you do not use it. It also uses about 300 MB of virtual memory right after start on my system, which can be a lot if you're constrained on memory.
I use Sql*Plus to run a few queries really quick. It is a console application (running in the "DOS window") and you can start it using sqlplus.exe. If you have a local installation of the Oracle database, the tool is somewhere there. MySQL has a similar tool (or so I believe).
You could try some alternatives to SQL Developer - such as
TOAD - but I don't use them, so don't know whether they would actually start faster or use less memory.