I would interprete it as:

Si vous me permettez de poser la question…

So for example

How old are you, if you don’t mind me asking…

Quel âge avez-vous, si vous me permettez de vous poser cette
question…?

After the relevant discussion I am not 100% sure if there is but the slightest difference between me/my asking structure. The difference is rather a grammatical one. In any case I think that French interpretations would be the same.

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I strongly suggest you to use (apart Google Translate which is very good for quick translations)

https://www.linguee.fr/francais-anglais

So for instance

https://www.linguee.fr/anglais-francais/traduction/if+you+don%27t+mind+me+asking.html

Also another useful web page is

http://www.wordreference.com/fren/

yet another one

https://www.deepl.com/home

You do not tell the context, whether a formal or informal question is expected, to whom you ask the question (tu or vous) but I would suggest anyway :

Si ma question ne te dérange pas / ne vous dérange pas, xxxx ?

The first part of your attempt was correct French: si cela ne vous dérange pas however, the end mon demandant doesn’t work in French. I believe “my asking” means my question so translates to ma question but you shouldn’t try to stick too much to the English form.

Here is another suggestion :

Si je peux me permettre (une question), xxxx ?

The most formal way to say it would be

Si je puis me permettre…

(The form je puis of the verb pouvoir is more formal than je peux and is used only in expressions like this one.)

You can also apologize for your curiosity by saying

Excusez ma curiosité, mais…

And more strongly

Désolé de vous enquiquiner, mais j’avais une question à vous poser…

and the answer will be «Mais non, vous ne m’enquiquinez pas» followed by the answer to your question.

Depending on the context,

Sans vouloir être indiscret,…

could work. For example :

Sans vouloir être indiscret, quel âge avez vous ?

It isn’t an exact translation but is idiomatic and conveys the same meaning. It is clear that a sensitive question is coming right after.

The most formal way would be:

Si je puis me permettre, (question)

Note that you could also use the interrogative form:

Puis-je me permettre de vous demander (question)?

I think this is as formal as it can be and is the one I would use.

I would say the “enquiquiner” proposal is really not formal.

I came up with ‘si cela ne vous dérange pas mon demandant’ but Google Translate is saying it’s ‘si cela ne vous dérange pas de demander’. Could someone help

In the phrase “my asking”, the word “asking” is grammatically a gerund:

The gerund is a verb which is used as if it were a noun … [for example] “Seeing is believing”

It’s formed from the present participle of the verb.

French verbs have a present participle (e.g. manger / mangeant) but I think they’re not used as gerunds i.e. as nouns. You could never say bon mangeant in French like you might say “good eating” in American English.

Instead I think the French tend to use the infinitive form of the verb, e.g. bon à manger (“good for to eat” also known as “good food”), or voir c’est croire.

So mon demandant is no good. If you want to use a noun in the phrase, you say ma question.

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Also I think that asking, “If you don’t mind…” is slightly rude: perhaps it’s imposing on you to decide.
So a slightly politer English version (which doesn’t ask you to commit yourself before you’ve even heard my request) might be to ask, “If I may, …”.
That’s where other answers are suggesting Si je peux or Si je puis.

Also, the distinction in English between “If I may” and “If I can” is, in French, the difference between pouvoir and permettre.
Again, I think it’s more polite to say “If I may permit myself to…” than “If you will permit me to…” — I think you’re expected to be well-behaved, to govern your own behaviour, to know what’s right and wrong, and to not impose that responsibility on others.
That’s where another answer suggests Si je peux me permettre instead of Si vous me le permettez.
Sometimes if you get a cold-call, i.e. a business phone call from someone you don’t know, they’ll explain the reason (i.e. why they’re allowing themselves to call you) by starting, Je me permets de vous contacter parce que…