There is no software workaround. The "Delete Save Data" confirmation screen in Nintendogs requires pressing L + R + A + B + X + Y + Start + Select simultaneously (or a subset including L) on the title screen. The L button is physically wired into the input matrix; the game code checks for its specific register flag.
Recommendation: Try the alcohol clean first (5-min fix). If the switch is physically snapped, the console recognizes it as permanently "unpressed," blocking the combo. Repair or use a new save slot.