Can I use capital improvements that I don't have receipts for the expenses to offset the capital gains?

Yes you can ... most people don't keep receipts religiously over 50 years however the IRS understands improvements  have to be made so make notes/keep photos and keep them for 3 years in case the IRS audits the return. 

if you don't have receipts how do you know their cost of the improvements? if this was your principal residence for 2 out of 5 years prior to sale, your entitled to exclude $250,000 of gain $500,000 if you are married.