Hiking and Day Walks in South island

Hi all, Me and my Wife is travelling to NZ in late sept specifically 17th to 1st October. Initially we wanted guided tramping but after researching I realise no one is operating during that period. :( anyway... I checked from DOC that many beautiful great walks are dangerous during that period and needless to mention doing it solo will be nuts.. I did further research and found that there are probably day walks like sealy tarns 4hrs return. I would like some advice from the experienced about doing such day walks solo. Is it safe? We are in late 20's and not pros. We are going to mount cook and aspiring for hike specifically since we can't do Milford for multi days