Does rim width affect what tire size I can use

Hello all...might be a simple question but as I am looking into upsizing my 13 inch rims to 14 inch ones, I thought I'd ask the following:
I have a set of SBP x 4.5 steelies and a set of SBP 14 x 5.5 rally wheels. I am trying to decide whether to go with 185/75r/14 inch tires or 205/70r/14 tires. From some reading I've done I am wondering if both tire choices are too wide for the original 4.5 rims? I likely will go with the 5.5 rally wheels . I have the centers and beauty rings for them and I also have a nice full hub cap as well. That said I am wondering if others are using the 4.5 inch wide rims for these tire sizes. Thoughts? With thanks.