The stress on the axle should be about the same, unless you are using a longer axle because of a laterally wider cogset (e.g. 128mm 7-speed vs. 123mm ultra-6 speed). I have broken three rear axles (solid French 120mm OLD, hollow/QR French 120, QR Campag. 126), but these were spread over more than 100k miles of cycling and never stranded me or threatened my safety.

To obtain a lower bottom gear, first see whether a smaller inner chainring is an option.
Next, determine how large a low gear cog your current rear derailleur can accommodate. As Chas. has demonstrated in other threads, you can often push this beyond the advertised specifications, which tend to be conservative, as engineering specs. should be.