[MRM]

It's been a long time since I've cut down a tree, but I grew up heating with wood and I can tell intuitively which way a tree wants to fall. It's hard to tell without being there, but I don't think it's going to fall the way you think. The branches don't have enough weight to affect its fall. The curve in the truck and the orientation of the trunk will determine where it will fall.

The issue with cutting it is more will it fall on something and break it rather than whether you're likely to get hurt doing it. Unless you're really obtuse or slow it's not likely you'll get hurt cutting one tree out of a pretty clear area. Is it going to hit something where it falls? If not and you're comfortable using a chainsaw then don't worry about it. If you need to drop it somewhere specifically then you better use a professional.

If you're comfortable with a saw, start by cutting a notch in the side of the tree you want to fall first. If you cut the notch less than half way the tree won't fall when you do the notch. Once the notch is in place, cut parallel to the ground on the back (un-notched) side of the tree. As you get close to finishing you'll hear the tree cracking and it will start to move. Just back up and wait for Gravity to take over. If it doesn't fall, carefully go back to the same cut and keep going. If you stay out from under the tree as it falls and away from the back of the trunk as it kicks back during the fall, you'll be fine. I wouldn't be worried about the tree hitting you. I'd be more worried about the saw kicking back or being pushed into the saw and getting cut.