Both are fine and have been used for decades, as far as I know. The OED on "unquote":
intr. Used as a formula in
dictation, etc.: terminate the
quotation. See quote v. 4c.
1935 E. E. Cummings Let. Mar.
(1969) 139 But he said that if I'd
hold up publication of No Thanks for
15 days he'd kill unquote a page of
Aiken.
1935, etc. [see quote v. 4c].
1969 New Yorker 11 Oct. 48/2 Then Mr.
Tanks announced the last downtown
stop. He said, ‘Madison Square Garden,
Penn Station+et cetera, et cetera, et
cetera, unquote’.
...
[4.]c. quote ... unquote: a
formula used in dictation to introduce
and terminate a quotation. Freq.
transf., in speech or writing,
introducing and terminating words
quoted (or ironically imagined to be
quoted) from the speech or writing of
another.
1935 E. E. Cummings Let. 3 Oct. (1969)
145 The Isful ubiquitous
wasless&-shallbeless quote
scrotumtightening unquote omnivorously
eternal thalassa pelagas or Ocean.
1950 ‘S. Ransome’ Deadly Miss Ashley
xvii. 198 She says, quote, ‘What girl
wouldn't?’ unquote.
1956 Times 5 Dec. 1/5 (Advt.), Today,
America, you sure are quote in the Big
Time unquote.
1958 B. Hamilton Too Much of Water xi.
245 But he did have, quote, a jolly
good reason for bumping off one
special person, unquote.
1961 P. Ustinov Loser viii. 140 He
expressed the personal opinion that
the picture was quote great for
America unquote.
1973 D. Robinson Rotten with Honour 8
The British…see too many people like
you in London.+ East Germans,
Bulgarians, and Rumanians, all of them
quote diplomats unquote
Best Answer
When reading a book aloud for recorded books, the reader never says "quote / unquote". Instead they indicate the quotation by a verbal change, such as a pause, or a change in the reading style or both.
The only time I've heard the quote / unquote construction used verbally is when one person is reading aloud another person's words during a debate or an argument.
For example, a television interviewer catching a politician in a lie by saying
In this example, the use of "quote / end quote" is an attempt by the journalist to inject some drama by verbally indicating he is quoting the senator verbatim.