Can I say to someone who converted to Islam, "Allaah will forgive your sins since you became a Muslim", without saying Inshaa' Allaah. Or do I say Inshaa' Allaah, Allaah will forgive you?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His Slave and Messenger.

Muslim reported in a sound Hadeeth that 'Amr Ibn Al 'Aas said: "When Allaah instilled the love of Islam in my heart, I came to the Prophet and said: Stretch out your right hand so that I may pledge my allegiance to you. He stretched out his right hand. I withdrew my hand. He (the Prophet ) said: What has happened to you, O 'Amr? I replied: I intend to lay down a condition. He asked: What condition do you intend to put forward? I said: I should be granted pardon. He (the Prophet ) observed: "Are you not aware of the fact that Islam wipes out all the previous (misdeeds)? Verily migration wipes out all the previous (misdeeds) and verily the pilgrimage wipes out all the (previous) misdeeds."
This is good news for all new Muslims that anyone who converts to Islam all the sins he committed before becoming Muslim are forgiven. This is made explicit in the following verse Allaah Says (what means): {Say to those who have disbelieved, if they cease (from disbelief) their past will be forgiven.}[Quran 8:38].
So, what you said to this new Muslim conforms to the Sunnah even without using the expression "Inshaa' Allaah" as the Prophet did not use that expression when he brought the good news to 'Amr Ibn Al 'Aas. But, if you say "Inshaa' Allaah", it is also acceptable as Allaah is not compelled to do anything. He acts by His Own Will. In fact, the adherence of the person to Islam, his guidance to the right path as well as the forgiveness of his sins all these are by the Will and Benevolence of Allaah.
Allaah Knows best.