A married couple where I work lied about being off sick, went for an interview at a company where our HR manager's husband works as the QA manager, he mentioned it to our HR manager as they both came from my employer and the result was them both being dismissed the following day.
Don't lie about it, take it as leave or be upfront.
Arguably the other company ought to sack or discipline the QA manager too if he can't keep things like that confidential. (see later on in this thread for example - someone got rumbled going for an interview and the company isn't happy with the person who gossiped him:
https://forums.overclockers.co.uk/threads/boss-making-my-position-untenable.18868416/)
It is pretty important from the POV of lots of companies that confidential stuff like that isn't spread about - that QA manager is a bit of a dunce and in plenty of places would be fired... I mean what else does he tell his wife at the other company, I mean if his wife is at a rival company then that is even worse - the hiring manager at his firm would likely be furious.
Though pulling a sickie is rather silly, it's generally a very bad idea to be "up front" about going for an interview unless you're very sure you're going to get it because if you don't get it then the damage is done and you're going to look rather weak - easy decision for your manager come pay rise and bonus time, just don't bother giving you a pay rise or a bonus and be able to reward the rest of the team with a larger share of the pot.
Also you're if you're unable to take half a day as leave then explaining that you're thinking about leaving and would like to attend an interview isn't, in most cases, going to do you any favours or suddenly get your half day (or whatever time off you need) approved after it was already rejected as a general holiday request!
I don't think you need either tbh... you can do this intelligently without having to take holiday at short notice and/or tell them about the interview. How many people go to the hygienist every 3 months? It doesn't cost much but you can easily book an appointment like that... that's your dental appointment covered... it is unlikely that you will get rumbled going for an interview but if it does happen then you're covered, you did go for a dental appointment and have the receipt to prove it... that you also went for an interview too... meh, you don't have a duty to tell them that. So long as you've done the work you're supposed to do/made up the time by staying late etc.. (or just taken half a day's holiday with the reason "dental") then what can they do... you said you'd be out for X amount of time, you said you had a dental appointment (which you did have) you also went for an interview... so what... call it your lunch hour etc..
I mean if you say "I could really do with taking a few hours Wednesday afternoon, got a few things to sort, Dental appointment, post office and some errands/other stuff etc... will be aiming to be back around 4pm and will work late to make up the hours" then much less of an issue... the interview was the "other stuff" you had to do, you're under no legal obligation to tell anyone you're going for an interview and if you got that overdue hygienist appointment in afterwards too then there isn't any lie about the dental visit either.
There is also working from home - have a delivery arriving(but in the morning) /relative visiting etc.. you can quite easily have those things be true and also pop out for the interview.
Generally though better to avoid the issues - lunchtime interviews are a good idea or early morning interviews - ideally you want to be able to say you're going to be late one day with no questions asked or just keep things vague. If you're going to use a specific excuse and are worried about being caught then either make sure it can be backed up or can't be contradicted... (something that can also be true alongside the interview).
Actually going for an interview isn't a sackable offence in itself so just don't be silly with things like pulling fake sickies (something that actually directly costs the company money). If not using holiday days then make sure you are making up the time by working late etc...
Bottom line though - it does you absolutely no favours at all in the vast majority of cases to tell anyone you're going for an interview - it is absolutely something that you should remain quite about until you get an offer.