Soreness: Wait to completely heal OR stick to schedule?

What are we supposed to do when it's time to work on specific part/muscle group but that part is still sore from previous workout?

Just a rough example...

Day 1: Upper body

Day 2: Lower body

Day 3: Core, cardio

Day 4: Upper body

Sometimes on Day 4 my (eg.) shoulders and my triceps are still sore from Day 1. I'm never sure whether I should...

A) Stick to schedule (do upper body workout anyway)? But that means I won't be able to lift as heavy / as many sets as I did on Day 1. Or...

B) Do a different workout, say a mixed cardio/low impact HIIT until I can lift my standard weights & reps?

Other notes:

- I always do warm-ups and cool downs; I often do extra warm ups and cool downs whenever necessary. It's just that I'm often sore for 2-3 days after strength training.

- I don't do anything intense--I'm a beginner and most of my workouts come from the FB Low Impact program (or similar independent workouts tagged "Low Impact", at difficulty levels 2-3). I don't even lift heavy, I just make sure I work out the affected muscles and keep good form.

Edited