Can I miss a week of reporting to unemployment in order to quit a job?

I am currently receiving unemployment benefits. My benefits run out in about a month, so I accepted a crappy job offer just to make sure I have something when my benefits run out, but did not anticipate it being so physically demanding and boring for little pay and little hours. I am still receiving partial benefits because this is a part-time job. I have only worked one day at the job. I have applied to other, more enjoyable and higher paying jobs and expect to hear from them soon. I would like to quit my current job, but know that since it is not the employers fault and I don't have a very good reason other than not liking it my unemployment will be terminated. I have read that if you stop claiming weeks of unemployment before your claim runs out you can still reopen the claim.

My question is when you miss a claim week does that week get deducted from your benefit year even though you did not get paid for it? Also, will I be able to quit my job during that week and have unemployment not know I ever took or quit the job? And lastly, when reopening the claim does it take a long time to process or can I just start back up receiving benefits again? When I initially filed my claim it look almost two months before I received my first payment. I do not want to be without income for that long again.

I have not turned in my I-9 and W4 paperwork to my current employer yet. If I am not able to not claim a week in order to quit the job without unemployment knowing I ever had it or quit it? I don't want to have to do that or to lie in any way, so does not having my paperwork in yet mean I didn't technically take the job and I can just have the employer not pay me for my day of work and consider it never happened?

I live in Michigan.

Thanks for your help!