can i replace ”viewing” by ”he viewed” in here?

Yes, you can replace "viewing" by "he viewed".

Andrew Cole, asset allocation director at Baring Asset Management, said, while viewing the sell-off as a correction.

Make it easier:
Andrew Cole said, while viewing the sell-off as a correction.

Since the subjects of the two clauses are the same,
Andrew Cole said, while he viewed the sell-off as a correction.
=Andrew Cole said, while viewing the sell-off as a correction.

In general, when the subjects of 2 clauses are the same,
we can use this form (v.+ing).

eg.
When I wait for my friend, I see a cat.

We can cross out "I"(after When) and change "wait" into "waiting".
Then the sentence will be "When waiting for my friend, I see a cat."

The "v.+ing" doesn't mean the whole sentence is in continuous tense.
It only means the sentence is in active voice.

If the sentence is in passive voice,
we can just cross out the "be".

eg.
When I am tricked, I feel unhappy.
Then the sentence will be "When tricked, I feel unhappy."

The "v.(in past participle)" doesn't mean the whole sentence is in past tense.
It means the sentence is in passive voice.

**However, we have to remember the two subjects must be the same.

唔應該改 .. 因為佢講o個句話既同時係睇緊個sell-off .. 所以先用while ..
既然係睇緊 .. 當然係要加ing ..

yes, you can:

the original text used a phase after "while" which is economical, because the subject was clearly stated (Andrew Cole). If "while" is at the beginning of the text, it is better to use "he view" instead of "viewing" for being an introductory clause.