Result: NO
Unfortunately, you currently can't install CFW on your console without external hardware :(
If you are unwilling to wait for a new exploit to be discovered (no estimated timeframe), the cheapest available method is ntrboot, which will require buying a compatible DS flashcart (roughly $8 USD). You can buy a preflashed cartridge from here (AliExpress, volatile link/listing, not always kept updated) or here (nds-card, static link, but more expensive)
If you are comfortable with soldering, you can also try hardmodding your console.