No, it shouldn't have any effect in this case. If you applied to multiple banks, then each new lender would see which other institutions recently looked up your credit history, i.e. which other banks you applied to. An underwriter might think that this could be a sign that an applicant has been declined elsewhere, which would not be the best start to the process. However, if everything was clearly fine about the application, then they would realise pretty quickly that you are applying to them for value, and not because you were turned down elsewhere.
Your bigger issue might be getting approved for 90%, unless that is not an exception to the LTV rule.
Best Regards,
Dave Curry, Irish Mortgage Corporation
https://ie.linkedin.com/in/davecurryirl