No, you can't. They are used in different situations.
There are two ways of making the verb 'have' a negative, depending on whether it is a main verb or an auxiliary verb (tenere or hacere in Spanish):
1. 'I don't have' is the equivalent of the Spanish 'No tengo' *
e.g. Do you have a sister? No, I don't have a sister.
2. 'I have not' / I haven't is the equivalent of the Spanish 'No he'
e.g. Have you seen that movie? No, I haven't seen that movie.
* Remember that you can also translate 'Yo no tengo..' as 'I haven't got..' , as in 'Have you got a sister?' 'I haven't got a sister'. In this case, the verb is used as an auxiliary verb.
..................................
'I have no....' is NOT a negative form of the verb. In English you can never make a verb negative by added the word 'no'. For example, in the sentence
'I have no money', the word 'no' belongs to 'money', not to the verb. You can separate the words in this sentence like this:
[ I have ] [ no money ]
This is the opposite of
[ I have ] [some money]
I hope helps.