Having a part-time freelance contract(not 業務委託) while contracted full time?

I'm currently employed full time as an engineer. I'm thinking of also doing freelance for another company on my free time, but sometimes this would require me to go to some factories to implement systems and so the company wants to have me as a part-time employee so that I'm covered by their insurance in case something happens or anything breaks.

Does anyone know if this could negatively affect my job?
I've asked my boss already before I accepted this job and he said as long as I don't sign any contracts it shouldn't be a problem, but I am now wondering about this part-time offer if it's feasible or not for.

I'm thinking of consulting a lawyer for this as well but would like to have an initial opinion from you guys.

by salmix21