A simpler solution would be to use component cables from to the TV same room, and HDMI to the TV in the other room. You're really unlikely to notice the difference in quality, and it'll be much less likely to cause problems.
You should be fine with a 10m run using a high speed 24 AWG HDMI cable, though probably not using a passive spliter.
Another option would to be get another satellite box for the other room. Probably not a lot more expensive than your other options.