Solution 1:

The benefit of Old English and Middle English orthography is that it is usually phonetic and the consonants are pronounced. Lots of people know how the letter k before an n does mean that you pronounce the k (hence the funny Monty Python pronunciation of knight).

The same is true for wl-, tough as it is to produce. I learned to pronounce it as written. According to the text commentary book to From Old English to Standard English, "Old English pronunciation," all Old English consonants were pronounced. In the book's examples are a few of the /wl/ words with their pronunciation as conventionally understood (I substitute slashes for brackets to not throw off link formatting):

wlisp -> /wlisp/

wlanc -> /wlank/

wlitan -> /wli:tən/

wlitig -> /wlitij/

Similarly, the /wr/ preserved to today with silent /w/ in words like wrist would be pronounced. In both cases, imagine starting the /w/ sound at the front of the mouth and then moving the tongue up to produce the /l/ or /r/. Following how Old English is conventionally taught, someone pronouncing /wl/ should move from the labial to alveolar approximate.

How do we know this? The study of Old and Middle English phonology over the past couple of centuries has combed Old English orthography, compared it to Germanic and other similar languages, and worked from texts (most notably the twelfth-century Midlands text Ormulum) that are consistent and meticulous about matching spelling to orthography. The disjunction of spelling and orthography only grows in late Middle English. (See below for an example where wr and r alliterate.) From Old English texts and some basic assumptions that authors within dialect groups would share phonological and orthographic features, it's clear that consonants literally represent their sounds and the consonants rarely shift in what sound they represent, to the point that we can see in texts when the pronunciation does change. If a vowel was present, the Old English spelling would add a vowel.

From these sources we're fairly certain that /wl/ and /wr/ were the pronunciations of wl and wr. At most, there is the stray argument that maybe (as Jacek Fisiak claimed in 1967) /wl/ was a single phoneme. If that were so, then this line in Beowulf wouldn't be alliterative:

wliteseon wrætlic; weras on sawon.

It's the /w/ that alliterates, not the /wr/ or /wl/. See also:

wlitan on Wilaf. He gewergad sæt,

What happened to these sounds? A recent treatment of phonology in Donka Minkova's text A Historical Phonology of English (2014) describes the transition from /wl/ or /wr/ to /l/ and /r/ in Chapter 5, "Consonantal developments in the second millennium." She cites early Old English examples of splitting the cluster /wr/:

wrohte ~ worohte ('wrought')

She also notes Middle English moves to simplify the sound:

wrynkul ~ runkel ('wrinkle')

Or to suggest that wr only slowly shifts to alliterate with r, as it does in the late alliterative text Piers Plowman (14th c.):

riche: ryden: wrathe

In contrast, the words with wl mainly dropped out of the language rather than being simplified in form. She cites one exception:

Words with initial /wl-/ were very rare in the OE and ME lexicon, and the only survival is lisp < OE * wlispian.

The pronunciation of /wl/ and /wr/ is so ingrained that Minkova need not cover how they would be pronounced in Old English; meanwhile, she carefully documents how the sounds would have changed into Middle English.

Solution 2:

As TaliesinMerlin mentioned, the pronunciation of "wl" in Old English is often simply reconstructed as /wl/. That may seem a bit tricky to pronounce, but when I try it, I think I can produce something approximately like [wl].

Polish is an example of an extant language that has "odd" clusters with [w]: there is a Polish word łgarza pronounced /wɡaʐa/, and there is even a word where /w/ comes between two consonants, płciami /pwt͡ɕami/. You could try to look into how /w/ is pronounced in Polish to get an idea of how it might be possible to keep it distinct from /u/ in these kinds of contexts.