The first is probably a Trichocereus huascha. I think you can plant it as is. I am not totally sure about Trichocereus, but their relatives often sprout roots from the areoles, so as long as some areoles are in the ground they root easily.

I think the only cactus called saguaro is the North American species Carnegia gigantea. I do not know what yours is, but it looks South American, could be some sort of Echinopsis. If the growth tip is damaged it will eventually grow offsets, cutting of the top should not make any difference. If it was my plant I would try to improve the growing conditions and induce offsetting that way instead of resorting to surgery. I do not like the look of cacti where the top has been removed, but that is just my personal taste.

Here is what I think it is. A tyrichocereus tersheckii also known as a Argentinian saguaro. It has been 5 years since the tip was damaged. That is why I am changing the situation, since their was no progress. Call me antsy.
Thank you, Mara

Here is a link that might be useful: Trichocereus tercheckii

FWIW, I'm with tjicken - since the possible A. saugaro is so small, I'd just leave the top and plant as is. offsets will pop out regardless and it might be better to leave the top alone. If the cat will let you touch it, that is. . . :-)

Could be T. terscheckii (Trichocereus is very closely related to Echinopsis). 5 years is a long time. Has i been outside in the ground, or in a pot?
The roots are just partially visible, are they as small as they look like?

It has been outside in the ground. It was planted right behind the other cactus in the first picture. Here is a better side view of the cactus .....and the cat. Part of me is thinking to toss it and get another since it has been so long. It might have gotten sunburned right off the bat when it was young and then the cold got the nib. It was one of my first cactus ansd I do not do a whole lot of protecting. It was unprotected during the 12 degree ni=ght this year, but it's tip was already damaged.

{{gwi:540389}}

The roots look small considering its age and the size of full-grown plants. I cannot see any fine roots either. I wonder if the problem lies there?

I still doubt that you will gain anything by decapitating it, if it had wanted to put out new growth it would most likely have done so.