Hi

No there is no problem with that.

For example there are many people who are lefty, but if they write with their right hand the only thing which will happen is that they will take more time to write and it may be difficult at starting. But with practice, that difficulty also goes away.

There are many people who train themselves in a label to write with their both hands.

So, there's no problem you can you can train your both hands to write as well, there's no harm at all.

Thankyou