Good questions - you're right to check each of these separately, because the CGT, stamp duty, Companies House and dividend positions all work differently here.
Capital Gains Tax. You're right: transfers between spouses and civil partners happen on a 'no gain, no loss' basis, and GOV.UK confirms you don't usually pay tax when you give shares to your husband, wife or civil partner. So there's no CGT bill on moving 20% of the shares to your husband now. He simply inherits your original base cost, and the gain is deferred until he eventually sells or gifts the shares on. There's nothing to report on your Self Assessment for the transfer itself where no gain arises.
Stamp duty. This depends on whether money changes hands. If you gift the shares for no consideration, there's no stamp duty. But if your husband pays you for the 20% (a sale), stamp duty at 0.5% applies where the consideration is over £1,000 - you'll complete a stock transfer form and pay the duty on the price paid. So the 'selling' versus 'gifting' distinction in your question really matters here.
Companies House / PSC. At 20%, your husband won't be a person with significant control - the threshold is more than 25% of shares or voting rights - so there's no PSC filing. You will need to update the company's register of members and issue him a share certificate, but no Companies House forms are triggered by a straight transfer of existing shares.
Dividends and the settlements legislation - this is the real watchpoint. Paying dividends in proportion to a genuine 20% shareholding is unobjectionable, and using your husband's basic rate band and dividend allowance is normal tax planning. Where HMRC's settlements legislation (the rules HMRC used in the Arctic Systems case) can bite is where the arrangement looks like income being diverted while you retain the underlying benefit - for example, if the 'gift' has strings attached, or the shares carry no real rights. An outright, unconditional gift of ordinary shares with full voting and dividend rights, where your husband genuinely owns and controls his 20%, sits on the safer side of the line - but the facts matter enormously, so take advice before you act, especially if the main motive is shifting dividend income.