cautiously in WordNet English dictionary

1. as if with kid gloves; with caution or prudence or tact
   "she ventured cautiously downstairs"; "they handled the incident with kid gloves"
   cautiously  carefully  cautiously  carefully 
   
2. in a conservative manner
   "we estimated the number of demonstrators conservatively at 200,000."
   conservatively  cautiously  guardedly  conservatively  cautiously  guardedly