No, this being so because when you say:

Nous faisons un cadeau à sa femme

It means that a group of people (including the person speaking) is giving a present to someone’s wife. So, in the case of an expression that describes a group of people in which each person does something to their respective “someone/something else”, you must say :

Nous faisons un cadeau à notre femme

And as you are asking about this case, consider the following:

• always use for the possessive adjective the same person as that of the subject,
• if each person does something respectively to more than one person, you also use the same person but in the plural.

For instance:

Nous faisons un cadeau à nos femmes

This is the second point, it means that each person has several wives…

On has more than one meaning in French so there is no single answer to your question.

With the intended meaning (each person does something to their respective someone), that would be:

• Chacun fait un cadeau à sa femme. Each one make a present to his wife.
• On fait un cadeau à sa femme. (generic on) Similar to the previous sentence. The usage is for husbands to make a present to their wives. Etymologically: (L’)homme fait un cadeau à sa femme.
• On fait un cadeau à nos femmes. (on for nous) We make presents to our wives.
• Nous faisons un cadeau à nos femmes. Formal/literary version of the previous sentence. We make presents to our wives.
• Nous faisons un cadeau à notre femme. This form is technically incorrect (there are more than one wife) but accepted as it rules out the case where more than one wife belongs to a single husband.
• Vous faites un cadeau à votre femme. (singular vouvoiement/singular) You make a present to your wife.
• Vous faites un cadeau à vos femmes. (plural/plural) You make a present to your wives.
• Vous faites un cadeau à votre femme. (plural/singular) You make a present to you wife. Accepted alternative in order to make clear there is a single wife per person, although it might be argued that it might mean a single wife is shared by several people…
• Ils font un cadeau à leurs femmes. They make a present to their wives.
• Ils font un cadeau à leur femme. (same as nous/notre and vous/votre: accepted alternative to avoid polygamy suspicion) They make a present to their wife.

A couple of sentences are grammatical but do not match the intended meaning:

• On fait un cadeau à ma/ta/sa/votre/vos/leur/leurs femme(s). (on for nous) : A group of people collectively make a present to someone else’s wife(s).
• Nous faisons un cadeau à ma/ta/sa/votre/vos/leur/leurs femme. ditto: we make a present to my/your/his/your/their wife(s).

Note that there is no case where we would say ses femmes because that would explicitely mean a single person has several wives.

To summarize, with possessives, you have to take into account the person possessing and both the gender and the number of what is possessed.

                         | one possessed     | several possessed
                         | masculine|feminine|
One possessor, me        | mon      | ma     | mes  
One possessor, you       | ton      | ta     | tes  
One possessor, him/her   | son      | sa     | ses  
Several possessors, us   |        notre      | nos  
Several possessors, you  |        notre      | vos   
Several possessors, them |        leur       | leurs 

Note that there are a few exceptions where mon, son, ton are used in front of feminine words.
See the OQLF BDL.