Nothing wrong with your version, but I (BE) think the emphasis is probably brought out better by saying "... because spending the whole day sitting down ..."
"Sitting all day (long) is unhealthy" can be interpreted (in terms of emphasis) to answer the question "for how long is sitting unhealthy?" (Two hours? Four hours? All day?)
"Spending all day sitting down is unhealthy" can be interpreted (in terms of emphasis) to answer the question "what is unhealthy if you spend all day doing it?" (Reading WR forum? Eating popcorn? Sitting down?)
[If you do all three of these at the same time, that's REALLY unhealthy!]