This question would ideally be answered by someone with a working knowledge of language teaching, based on studies about best practices. I haven't been able to find something like that, so I'll just give you my opinion.
You ask if you can always use "present perfect" (that is, the tense called pretérito perfecto) instead of the "simple past" (that is, the pretérito indefinido). That would be wrong and, for most Spanish hearers, it would sound weird. Not so much in Spain, where the compound preterite is far more common, but surely in Latin America. That's a fact: the two tenses serve different purposes.
Now, if this is just a temporary approach, and it helps you build up your confidence while speaking, then I'd be all for it. The key is: does it actually help you? Will you then find it easy to switch to the correct verb forms? That is up to you. You need to be aware of what you're doing and, in time, start incorporating those irregular verbs into your speech (maybe not all at the same time). Otherwise you'll just become fluent in Weird Spanish.
Personal anecdote: I'm learning German. As in Spanish, each verb is conjugated for person and number, and also as in Spanish, there is a compound preterite and a simple preterite. Unlike Spanish, most German informal speech uses the compound tense. But for some common verbs (the equivalents of have, be, do, etc.) you must use the simple past when it's due. As it happens to you with Spanish, I'm now at the point where I employ the compound tense for all past actions, except for those verbs, but I don't know many of the (mostly irregular) simple preterite forms yet. I know I'll have to learn them some day.
So I'd say: speak as you can, for now, but don't put off learning the correct verb forms. Start with just a few of the common verbs (decir, hacer), incorporate them into your speech, and keep at them until they come naturally. Then incorporate some more verbs, and so on. They're not so many and you can use them in fixed phrases. For example, it's not that difficult to remember to start a bit of reported speech with Yo dije or Él dijo. After a while it should just come out automatically.