Mr Hamilton said he is "very concerned" about the implications a Yes vote could have on the company, which employs 200 at its manufacturing site in Blantyre.
While Daysoft enjoys a "great relationship" with Royal Bank of Scotland (RBS), he has scheduled talks with a bank based in England with a view to switching before the poll on September 18.
Mr Hamilton is frustrated the cost of separating Scotland from the UK has not been fully detailed.
And he is unhappy RBS cannot guarantee his firm's deposit will be underwritten by the Bank of England in light of a Yes vote.
The latest accounts available for Daysoft at Companies House, for the year ended December 31, 2012, show that it had closing funds of £2.86 million.
Mr Hamilton said: "We've had to go into discussions with the bank about the security of our own cash.
"And the [independent] advice we are getting is not to bank in Scotland because there is no bank of last resort. So we are actually looking seriously right now at our banking arrangements."
Audited accounts for the year ended December 31, 2013, show Daysoft booked profits before tax, interest and dividends of £1.58 m. Sales generated by the firm, which designs and makes its own lenses, increased by 12 per cent to more than £10m.
Mr Hamilton welcomed the "substantial growth" enjoyed by the firm over the period.
However, he admits uncertainty over the currency and VAT arrangements an independent Scotland would adopt were also causing him concern.
Mr Hamilton said: "I've got no agenda other than to see Scotland flourish, but I'm worried about the method we use for that.
"Although we have a global market, our home market is 60 million. If we go independent the home market shrinks to five [million].
"I know there are those who will say it won't make a difference, but I know that it will."
RBS declined to comment on Mr Hamilton's views. A spokesman said the bank was politically neutral and will respond to the referendum and any decisions made by government and regulators should there be a Yes vote.
Daysoft ships 2,000 orders of contact lenses to wearers around the world every day, with the company receiving orders on its website at a rate of one every 20 seconds. Consumers can place orders in different languages and pay in different currencies.
Mr Hamilton said the firm has major competitors such as Bausch & Lomb and Johnson & Johnson but is able to take them on by being the only manufacturer to sell directly to consumers online.
It does not sell its lenses to high street chains, but does supply independent opticians.
Mr Hamilton said: "Our business model is distinctly different in that we have cut out the costs associated with that route to market. We haven't excluded using high street retailers, but we have avoided the big UK multiples because they exert too much pressure over small businesses."
The period covered by the firm's latest accounts saw Daysoft take steps to extend its manufacturing site. It has occupied the new building, which expanded the site by 20 per cent, in January.
The latest addition means the firm has exhausted its potential for growth at the current site, having carried out two extensions since acquiring the building by cash five years ago. The company is currently able to produce 1.4 million lenses per week or 70 million a year.
Mr Hamilton said: "If I could double the factory tomorrow I would do that. We're still looking for more space."