im about to give some of the best advice you will ever get regarding knackered 45's,my trade is spraying cars and my job has proved useful to clean up crap vinyl!
fistly you will need to buy some products,that are quite expensive,but will last you for years.
1. 3m superfine denib wet & dry paper
2. 3m finnesse polish
these 2 will set you back about £40,however there are cheaper versions,but i use these all the time and are the best quality.
technique
1. take a piece of the paper and dip it in soapy water and lightly rub (flat) the vinyl surface,you dont need to press to hard,go around the surface 2 or 3 times,avoid the label though.
2.dry the vinyl,it will look matt,but you have just taken out all the scratches and scuffs.
3.take a soft cloth,apply some finesse polish,then just keep rubbing that vinyl until it shines,apply as much polish as you need and keep going
and thats it.
once you have the knack,you can save an old piece of vinyls life.
bare in mind ive done this for years,and believe me i can make a a bollocks record play and look like new again!
if i get chance i will post a before and after pic of a refurbed 45.
get rubbing!