Multiple regression with non-normal data in minitab - help

I am aiming to assess the effect of BMI (continuous) on certain biomarkers (also continuous) whilst adjusting for several relevant variables (mixed categorical and continuous) using multiple regression. My data is non-normal which I believe violates one of the key assumptions of multiple linear regression. Whilst I think it can still be performed I think it affects significance testing which is an issue for me. I think I can transform the data and then perform regression but I'm not sure and also have some questions regarding the implications of this. I have tried Box-cox transformation but MiniTab is unable to do this as some of the values are zero. I have performed Johnson transformation (which I think is a variation of Yeo-Johnson transformation) and now have columns of normal looking transformed data but - A) is this the right thing to do, B) if so do I need to do this for all non-normal variables or just the outcome variable, C) how will this effect the beta coefficient in terms of calculating the final quantitative effect BMI has on the variable given that I’m using transformed data and not the original? I could potentially change my outcome variable to a categorical variety and use multiple logistic regression but not sure if/how this helps. I am not thinking about non-linear regression at this point as this seems more complex (perhaps too much for me) and I’m hoping to solve this issues without in the first instance. Any help would be much appreciated.

Kind regards