Whether you choose a credit card for no credit or a regular financial instrument, whenever a new credit card gets added to your reports, it will improve your credit mix significantly. It also results in a little bit of improvement in your credit score. The bottom line here is diversity.
Yes, diversity of accounts is not exactly a very significant credit score category but it does affect your FICO scores. It accounts for 10% of this score but you can grab this entire percentage by making your credit mix more diverse. Opening a new credit card account or any revolving account is going to help your credit scores a lot. When applying for any credit cards with no annual fee, keep this aspect in mind. But if you already have a diverse credit report, having a credit card or adding another credit card account is going to have little to no effect.