When did Catholic churches start using wooden clapper during Holy Week?

They were used at least in the 13^th century, when William Durandus (1237-1296 A.D.) wrote his Rationale Divinorum Officiorum, book 1 (of 8) of which is translated into English as The Symbolism of Churches and Church Ornaments.

Philip Goddard, Festa Paschalia: A History of the Holy Week Liturgy in the Roman Rite, p. 164n95 cites

Rationale, Lib.VI lxxii, 3-4 (Dura, p. 512)

which is:

3. In his vero tribus diebus silent campanæ, quia tunc siluerunt Apostoli, et prædicatores, et alii, qui per campanas intelliguntur. Sonus autem campanarum significat sonum prædicationis, de quo dicitur: In omnem terram exivit sonus eorum (1); non enim jam circuibant evangelizando vicos et urbes, sed hymno dicto, exierunt cum Jesu in montem Oliveti. Quibus cum Dominus dixisset: Ecce appropinquat qui me tradet, præ tristitia dormitaverunt, et a laudibus conticue runt; unde et a Completorio, sive a Vespera qua Dominus traditus fuit, campanarum silentium inchoatur. A Vespera autem qua Dominus traditus est, quando videlicet discipuli fugerunt, cam panis silentium indicitur.

4. Alii videlicet ad Primam hujus quintæ feriæ, et non ulterius,pulsant campanas; fit tamen signum cum tabula. Primo, ad significandum Christi humilitatem, qui se abscondit, et usque ad mortem et sepulturam se humiliavit; ligni quidem usus humilior æris sono hoc ostendit, et inde Ecclesia orientalis usum udbuc tenet lignorum, et ut populus humilior reddatur. Secundo, per signum tabulæ terrorem accipimus. Tabula ergo percutitur, quia magnus timor Apostolis a Judæis incutiebatur. Tertio, per lignum in ligno malleum, scilicet in tabula suspensum, intelligimus Chri stum, qui est lignum quod plantatum est secus decursus aquarum (2), qui in Crucis ligno pependit, et pendens orabat et prædicabat, dicens: Pater dimille illis, quia nesciunt quid faciunt (3). Cum ligno autem tantum pulsant, quia tunc solus Christus prædicator habebatur, et solus torcular calcavit. Quarto, per tabulam ipsam, lignum fructiferum, scilicet Christum; per malleum, quo tabula per cutitur, lignum prævaricationis significatur.

(1) Psal. 18. (2) Psal. 1. (3) Luc. 23.

English translation:

3. But in these three days the bells are silent, because then the apostles, and the preachers, and others, who are understood by the bells, were silent; And the sound of the bells signifies the sound of the preaching, of which it is said: Their sound hath gone forth into all the earth: and their words unto the ends of the world. [Ps. 18:4]; for they no longer went around preaching the gospel to the villages and cities, but having sung a hymn, they went out with Jesus to the Mount of Olives. And when the Lord had said to them, Behold, he who draws near to betray me [Mt. 26:46], slumbered in sadness, and fell silent from the praises; whence also the silence of the bells begins at Compline, or from the Evening on which the Lord was delivered. And from the evening on which the Lord was delivered, when, to wit, the disciples fled, a silence of bread is summoned.

4. Others, namely, on the first of this Thursday, and not further, ring the bells; he makes a sign with a tablet. First, to signify the humility of Christ, who hid himself, and humbled himself even to death and burial; the use of wood indeed shows it to be lower than brass in sound, and thence the Eastern Church maintains the use of wood, and that it may be rendered lower than the people. Secondly, we receive an alarm via the sign of the tablet. The tablet therefore is smitten, because great fear was struck among the apostles by the Jews. Thirdly, by a hammer on wood, that is, hanging on a tablet, we mean the Christ, who is a tree which is planted near the running waters [Ps. 1:3], who hung on the tree of the Cross, and hanging on, prayed and preached, saying: Father, forgive them because they do not know what they do [Lk. 23:34]. But with wood they beat only, because at that time Christ was considered the only preacher, and only he walked on the winepress. Fourthly, by the tablet itself, the fruitful tree, namely Christ; by the hammer, by which the tablet is cut, the wood of transgression is signified.