It's a good and valid question so dangerous would not be how I'd describe your knowledge.
You should not have a problem with this. What I recommend is if you ever have a concern with the mixing of greases and cleaning out the old prior to putting a new one in isn't possible, then accelerate your greasing times for the first little while. What this will do is allow the new grease to help over take the old. For example,in a bearing you have old grease residing, when you pump in the new grease, it will mix, and if there is some sort of mixing problem, while under normal interval greasing, this would allow the problems to exacerbate, but if you re-grease at an accelerated rate, this would help "purge" out the old grease, and give you a better feel as to how the new grease is going to hold up.
As for the pins and such, as you pointed out and this is very common, grease is squeezed under extreme pressures on pins and bushings and will not stay put. Because of this, you shouldn't see any problems with mixing as there won't be enough left from the old to interfere with the silver streak. I think you'll actually see an immediate difference with in the first day as to how this stuff will work in comparison to regular grease or silicon for that matter. The base gets tackier the more it is used and will adhere to the pins for a much longer time.
After you've ensured that the grease isn't being affected by the old residue, you obviously can adjust your greasing intervals to what ever level you need to based on what you are seeing.
Hopefully this helps.