It would involve providing cash for kidnappers or extortionists. They want small bills in large amounts, nonsequenced, which you swiftly supply to the victim’s relatives for an modest 
fee.
Would this be legal, and could it be profitable?
I suppose you could take issue with the tense of the text of the law, i.e. that before the money was delivered it was not specifically associated with the random, but if your business model is charging a fee to random payers to exchange electronic payment or large denominations for “small bills in large amounts, nonsequenced”, authorities are going to take a pretty dim view, and in the case of any interstate transfers will probably go after you using the Racketeer Influenced and Corrupt Organizations Act (RICO), likely with good effect given the broad applicability of RICO and the fact that your business is entirely predicated upon kidnapping and extortion even if you aren’t in specific conspiracy with the perpetrators.
If if you are keeping large amounts of case in small denominations around without being the proprietor of a bank or credit union, you can also expect to get hit with civil forfeiture actions repeatedly and frequently, requiring you to prove that your stash of cash is not involved in illegal activity. Good luck making that case to the court even with the best legal representation your fives and tens can buy.
Also, cash money is surprisingly heavy and bulky. Several million dollars in small bills will easily fill up multiple large duffles. How many assistants can you find to haul this stuff around without helping themselves to a share of the loot?
Stranger
Sure, money changing is done all the time. How is a change dispenser to know if the quarters are for the juke box, the washing machine, or the unlicensed slot machine 'round back?
You’re 10 years too late.
Now all the hip with-it extortionists & kidnappers want Bitcoin. Big duffles of cash are sooo last century. And heavy. As was pointed out upthread.
Just so I understand right, your business is there to bail out victims’ families who need large amounts of small-denomination cash but cannot obtain it in a short time? I’m not sure why the families could not just go to a bank and request cash, unless the bank is only full of $100 bills or similar high-denomination bills.
The other issue that I think is a problem is that kidnappers’ demands are pretty unpredictable. They could demand so many different things (one wants gold, one wants Bitcoin, one wants small-dollar bills, etc.) that your business might only cover 30% of such demands.
Also, you’d have to have a LOT of abductions going on to make this business profitable.
How much money in small bills can you withdraw from the bank without word getting passed to some legal agency?
Banks routinely ‘trade’ old bills that are worn or damage to the Federal Reserve and receives the equivalent in newly printed currency, which is why the bills you get from the bank are often crisp and uncreased. Most new bills are also generally packaged in sequence, which allows them to be easily inventoried upon delivery prior to being distributed to the public. Most bank branches have enough cash around to support daily exchanges; even for a large bank this is probably just a couple million dollars, and will be mostly in $1, $20 and $100 bills. No bank is going to maintain giant piles of $5, $10, and $50 bills just waiting for someone to come in and ask for large amounts of odd denominations.
Whenever I see a kidnapper in a television show or movie demanding millions of dollars in low denomination, non-sequential bills to be delivered within hours I know that the screenwriter is just repeating a trope they’ve heard from other media because it would basically impossible to collect together this amount of money in a few hours even if scouring all local bank branches. Most kidnapping-for-random schemes tend to involve people who are involved in the drug trade or other nefarious activities because they already have cash on hand and aren’t inclined to involve law enforcement. Or else they are nihilists ‘kidnapping’ the trophy wife of a millionaire philanthropist who is embezzling money from the charitable trust that he manages.
Stranger
You have to fill out a form to withdraw (or deposit, FYI kidnappers) over $10k but that’s for forensic tracking reasons and not to prevent the withdrawl. The bank probably has a limit by policy.
If you had a business that dealt in lots of cash, this might be a possible side business. For instance, many legal marijuana dispensaries deal only in cash because of issues with the credit card and banking industry. A dispensary could offer $10K in random bills for $10K in $100 bills with a X% service fee. As long as they didn’t advertise it as being for illegal purposes, it seems like it would be okay. It might be like how smoke shops sold water pipes, but they said they were for use with tobacco. If you mentioned any sort of use with illicit substances, they wouldn’t sell to you.
But for this money changing service, it doesn’t seem like there would be anything illegal about it. I would think that getting money to pay kidnappers is legal. Kidnapping is illegal, but I don’t think paying kidnappers is illegal.
Depends on the country, I guess.