I have never owned either a Henry or Marlin lever action, so can not help about that - but your comment about "prefer the cross bolt safety" - what you get used to, I guess. My 1955 Winchester 94 does not have a "safety", at all - I think that is the case for 100 years of external hammer, lever action rifles - so, if you have a loaded round in the chamber, you can lower the hammer to a "half ####" position - short of a substantial blow on that hammer, that rifle not going to fire - you use your thumb to pull that hammer back to "full ####" to fire it. I suspect various trigger block safeties that were introduced will still rely on the sear from the trigger to hold back the hammer - so same abusive "blow" will allow that sear to let go / break / "jump off", and the gun would fire with that type of safety "on". There used to be a thought that a rifle's safety was between the shooter's ears - was not really a device on the rifle - most devices on a rifle have at least one way to get broken, to malfunction, to be forgotten, to allow something unexpected to happen. About the most un-nerving to me is the "backward" safety lever on the CZ and BRNO rifles here - pull the lever back towards the butt to fire - push it forward towards the muzzle to be "on safe" - exactly opposite to most other North American built rifles - so, which way should the safety lever be moved, to be "on safe"?
When I was about 12 or 14 (?) (1967 or 1969) and old enough to get my own licence and carry my own rifle for deer hunting, my Dad got me a No. 4 Lee Enfield. My hands were not big enough, or perhaps not strong enough, to manipulate the safety lever on the left rear of that action - so I was shown NOT TO USE IT. A rifle can not fire if the chamber is empty. You can partially load a round into the chamber, but the firing pin is not cocked on those rifles until the bolt is pushed all the way forward - so is how I would carry it - either with an empty chamber and the bolt closed, or with a round partially chambered and the bolt handle up - was as fast for me to cycle that bolt, or to slap that bolt handle forward and down, as it was to roll the thing over and manipulate that safety lever.