I am a bit confused here as to how a 4K loan will negatively effect your credit score if payments are made on time. FICO scores are based upon how well you borrow. If you borrow, pay back on time, your score will not go down. Perhaps a bit in the short run when you first secure the loan, but that should come back quickly. In the long run it will help improve your score which seems like it would be more important to you.
Having the provider finance your loan will probably not show up on your credit unless you fail to pay and they send to collections.
If the score is so important to you, which I think is somewhat unwise, then use a credit card. With a 750 you should be able to get a pretty good rate, but assume it is 18%. In less then 9 months you will have it paid off, paying about $293 in interest. You could consider that a part of the cost of doing business for maintaining a high credit score. Again not what I would advise, but it might meet your needs.
One alternative is go with lending club. With that kind of score, you are looking at 7% or so. At $500 a month, you are still looking at just over 8 months and paying about $100 in interest. Much less money for improving your credit score.
Edit based upon the comment:
"My understanding is that using a significant portion of your available credit balance is bad for your credit, even if you pay your bills on time."
Define bad. As I said it might go down slightly in the short term. In three months you will have almost 33% of the loan paid off, which is significantly lower then the original balance. If you go the credit card route, you may be approved for quite a bit more then the 4000, which may not move the needle at all. Are you planning on buying a home in the next 90 days? If not, why does a small short term dip matter? Will your life really be effected if your score goes down to 720 for three months?
Keep in mind this is exactly the kind of behavior that the banks want you to engage in. If you worship your FICO score, which gives no indication of wealth then you should do exactly what I am suggesting.