Six Foot Track over 26/2 to 1/3 (Viable in Rain?)

Hey all,

Hoping to do the Six Foot Track for the first time this weekend, but the forecast is looking very rough:

2-20mm rain tomorrow
1-15mm rain Saturday
0-5mm rain Sunday

This will be our first time doing the track, starting at the Western side and ending up at Katoomba. Any advice on if this is still viable given this heavy rain? I know the climb up at Katoomba is very steep, so I do have concerns about if its muddy, given it will be wet all weekend.