As someone else pointed out, you are not geting an equity loan you are getting a first mortgage. So you must meet the requirements of such mortgages and that likely means a minimum loan amount.
BUT.. that is a doable thing.. and in a way that will actually help your credit.
You borrow the minimum amount needed that the bank will loan you against your house. Lets say its $100000 at about 4%,,, Your payment will be about $1000 /month
You only need $25,000 so your payment would have been $250.
You repay 50% of the loan the next week so now you only owe $50,000 and change and you have $25,000 in the bank after you finish spending the $25,000 on repairs.
your payment is still $1,000 per month but your annual interest is only about $1500 or a bit over $100 per month more then the $150 you would have owed on the $25,000 lona. BUT.. it will all pay itself off in about 10 years or so.
So,you use the $excess money in the bank to help with the mortgage payment until your income increases to the point where you do not need it (your note is fixed but hopefully your income will increase a bit each year).
All of the interest is deductable plus you will earn a small amount of interest on the $25k deposit.
Lastly, your credit score will improve with continued and regular payments.
Do the application with a local bank.. that way you may get a few extra perks like direct transfer, extra interest amounts and so on.. Most of the internet ads are bogus anyway.